The first number is the focal length. There are probably a lot of books that can explain a focal length technically, but the main thing you have to know is that the lenses with a smaller number show more in the photo than a higher numbered lens at the same distance. For 35 mm cameras, a 50 mm lens is considered normal. Everything in the picture is pretty normal or not distorted.
Wide angles are nice for landscapes, etc.
They act sort of like a magnifier in that they bring things that are far away up much closer. The distortion with a telephoto lens is more a compression effect and it is probably the best kept secret for a horse photographer. Most amateurs can't understand why their horses have long heads and short back legs, but it is because they usually use a 50mm lens to take the photos. The other numbers on a lens are the largest aperture opening available for that lens. Sometimes with horses you need to keep the shutter speed up because of movement.