The first thing you have to do before finding out what a distortion pedal is really define what distortion is. To give you the best definition that I can offer, it is simply the crackling noise you would get on the guitar. It is most commonly found in the rock genre of music. It has a very dirty sound to it and is not quite as clear and crisp as older music.
The distortion pedal is actually what allows you to adjust the amount of distortion that you would apply to the tone on your guitar. Some songs may have a lot of distortion, and there can be more or less played in specific areas of a song. For example, verses may not have any distortion, while the chorus has a lot applied to the guitar tone on the song.
So how much is a good amount of distortion? To be quite honest, no one can actually tell you what a good amount is.
There are plenty of people who really like the distortion in the tone of their guitar.Others really do not like much, if any. It is all up to you when you are writing music. In fact, there used to be a very popular guitar player in a band that took older and less quality amps and played his music regularly on them. He would actually punch holes in the speakers which gave it a more distorted sound. That is what he thought sounded good. People seemed to like it because it had a unique sound.
It really caught on in popularity, but I would not recommend punching holes in your speaker to get a unique distortion sound. Instead, just use a distortion pedal! Pricing on a distortion pedal varies greatly. Generally, one hundred dollars is about average on what you might pay for a pretty good one. Generally distortion pedals almost last you forever because they are not something that you will always use on every song in most cases.
A lot of songs simply do not use any distortion at all so you would just turn it off on your pedal and never have to use it. However, if you are really trying to mimic a song that uses distortion, then having a pedal will make your life much easier to truly get an accurate sound.