Learn the important facts in this easy to understand article.

Focal Length determines the field of view of our camera. The human eye has a field of view that is comparable to that of a 50mm lens on a 35mm film camera. We therefore consider 50mm the standard focal length.
Lenses with a very short focal length (wide-angle lenses) have a much larger angle of view and thus, fit a wider scene into our frame. Lenses with a long focal length (telephoto lenses) have a much narrower field of view. They pull far away things in close.

Tip: Since our eyes are so used to the 50mm field of view, we usually find photographs shot with extreme telephoto or extreme wide-angle lenses much more interesting.
 

Transformation of the Visual Space

Telephoto lenses compress the visual space, causing foreground and background elements to appear closer together. In contrast, wide-angle lenses stretch the visual space. As a result, foreground elements appear greatly exaggerated, even distorted, while the background elements seem to recede.

Long:

We create compelling images by using the transformation of the visual space to our advantage.
When we take a photograph of a group of people in front of Half Dome, we could step back a few meters forcing us to zoom into the scene to fill the picture with our group again. Half Dome will now appear much larger, looming over the heads of our group of fellow travelers. People at home will be in awe of the scenery. A very common mistake is standing too close.
(Example: La Purisma de Conception)

Short:

Alternatively, we may decide to use a short lens and get really close to our subjects, to create an intimate perspective, exaggerating the subject and making it appear larger than life, while the background becomes diminishingly small.
(Example: Yucca Flower)

Use it:

With this awesome tool at our disposal, we can transform the world to our liking and create images that others will find pleasing without knowing why. Focal length is thus one of the most important creative tools in our arsenal. It is much more than deciding if we want to zoom in for the sake of getting closer to an otherwise out of reach subject.

Influence of Focal Length on Depth of Field

Most photographers believe that lenses with a shorter focal length (wide-angle) have a larger depth of field, while telephoto lenses have a shorter depth of field. Although this is incorrect in absolute terms, it certainly appears to be true. In reality, only aperture determines depth of field, but since the perspective is so grossly different, distant objects will appear much smaller on the image taken with a wide-angle lens. When we magnify distant objects to the same size, they are out of focus by the exact same amount. In the extreme case, the distant objects will become smaller than our pixel and we can truly say that wide-angle lenses have a larger depth of field.

Focal Length Multiplication (Crop Factor)

For decades, 35mm was the standard film format. When you bought a 50mm lens, you already knew what angle of view you would get with that lens. All was good, until the fabulous engineers introduced digital SLR cameras. Everybody was happy, but our world also got slightly more complex. We now had to consider something called crop factor.

Why:

Building sensors (CMOS chips) of the same size as 35mm film is still extremely expensive. Cameras with such sensors cost more than many photo enthusiasts are willing to spend. The simple solution is to use smaller sensors.

Impact:

Using the exact same lens, the smaller sensor now “sees” a smaller portion of the image. Assume that I recorded the Image with a 35mm camera at a certain focal length (about 50 from the looks of it). Many prosumer and consumer Canon cameras have a crop factor of about 1.6 (shown with the red square). The narrower angle of view is similar to cropping the edges off, hence crop factor. Full frame cameras are cameras with sensors of exactly the same size as 35mm film. They do not have a crop factor (crop factor of 1.0)

Calculation:

In order to obtain the exact same field of view, a camera with crop factor therefore requires lenses with shorter focal lengths. A 30mm lens will give you about the same angle of view a 50 mm lens gives on a full frame camera. (50mm/1.6=31.25mm). A 30mm lens will have a wider apparent depth of field, which is good news for landscape photographers and bad news for portrait photographers.

Limits:

As if the life of a photographer is not difficult enough will all this depth of field stuff, it gets even harder once we consider the other end of the scale.
While depth of field limits our image sharpness on the one end, diffraction limits our sharpness on the other end. In order to increase sharpness, we need to use wider apertures (diffraction), but then we lose depth of field (range of sharpness throughout the image).

Pro’s and Con’s:

Just remember the crop factor in your lens buying adventure. A wide-angle lens will behave like a normal lens when used on a camera with crop factor.
Fortunately, the lens people have already reacted and extended their portfolio towards the ultra wide spectrum. Better yet, a cheaper, lighter 200mm lens on a camera with crop factor will behave like a 320mm lens on a full frame camera. A 300mm lens can easily cost twice as much and can weigh as much as a tank.

If you are uncomfortable with all this information, take comfort in the fact that it gets easier from here. At the end of the series, I will introduce some basic examples of lens buying decisions that will make it easy for you to pick. Things often get very technical, but fortunately you do not need to know all this to take good pictures.
Just remember the crop factor of your camera, as it will come back to haunt you when you are calculating exposure times.
 

Prime Lenses vs. Zoom Lenses

my lovely 50mm prime A prime lens has a fixed focal length whereas a zoom lens has a variable focal length. With prime lenses, you need to change the lens every time you want to change your focal length, and even then, you only have fixed steps available. For instance you have 30mm, 50mm, 80mm 135mm prime lenses.
Zoom lenses on the other hand offer great flexibility. A single lens can cover the entire range (or more) of those four prime lenses, without you ever having to change the lens.

Why Prime Lenses:

It seems that the zoom lens is the clear winner, but do not dismiss prime lenses just yet.
A prime lens takes excellent images. There are no moving parts, making them very precise. Having just a single focal length also makes it much easier to optimize the lens and squeeze the best performance out of it. Especially older zooms had many problems with picture quality throughout the entire zoom range and over the entire picture. These days expensive high quality zooms are available rivaling the performance of some prime lenses, but not everyone can afford them.
Primes get the best bang for your buck in terms of image quality. They are much cheaper than zooms of comparable quality. When you do a lot of studio work, there really is no need for anything but prime lenses.

Why Zoom Lenses:

my favorite zoom Zooms are much more popular with travel photographers such as myself, who need to keep the overall weight down (less lenses) while maintaining flexibility. Their versatility is very appealing, but keep in mind that nothing comes free.
Unless you have the luxury to buy lenses that cost as much as a small car, you will most likely have to trade off image quality for flexibility. Depending on your needs, you can minimize the downside by doing your homework (or just skipping to the last section of this article, where I will give some examples).
I only own one lens, a cheap plastic 50mm f/1.8 from Canon, that cost me less than $80. It beats all my other lenses, including my only L glass, the 70-200mm L f/4 in terms of sharpness.

Zoom Range:

Zoom lenses have a range. For instance 70-200mm or 18-200mm. While the latter seems much more appealing, keep in mind that image quality is often inversely proportional to zoom-range (for the same money). This is because it is harder to optimize a lens for a wider range.

Summary

Focal length determines our perspective, cost and artistic possibilities. We use a standard lens to mimic the human angle of view. We find it easier to accept these pictures with our subconscious mind as depicting reality, since we are used to this angle. Our own vision correlates well.
Wide-angle lenses have a much wider angle of view. They create tension in an image and may puzzle our viewers. They are great tools for landscape photographers or for indoor shots, where space is limited and we cannot step back to frame a picture. They do have the tendency to seem unreal though.
Telephoto lenses are great for wildlife and sports photography. The narrow view lets us get close to the action.
 

Tamron has a nice online tool designed to help you get a better feeling for focal length.
Tamron Tool

It is important do decide what you wish to photograph. People will not look flattering with a wide-angle lens. We need to move very close to our subjects, which magnifies the features closer to us, and thus, distorts facial and body features.

A good all around lens that I can recommend: