Ultimately, you exist in your present form due to mutation. It's the driving force of natural selection and the reason we aren't all single-celled creatures living in rock pools. When the DNA in your cells (the biochemical which tells the rest of your body how to be structured) gets copied to make new cells, it gets mutated in the process, causing new features in you, the person.
When a DNA strand is split and copied, there are several steps and several different "enzymes" (biological machines) in charge of different stages of the copy. Rather than a smooth photocopying process, there are at least 9 known parts to the copying process, each with its own enzyme. If something goes wrong during this complex copy process, we end up with a mutation/new sequence in the DNA sequence.
There are two main types of DNA mutation: Substitution (where one of the DNA building blocks is swapped for the wrong one) and Frameshift (where an extra block is added, or an original block is missed out, and the entire sequence is out of alignment.
There are four main sources of DNA mutation:
1) Simple copying errors. With so many chemicals floating around, winding and unwinding about each other, it's no surprise that sometimes the wrong building block gets inserted into the DNA. The four building blocks available are called A,G,T & C and they're all fairly comparable in size, so they can get mistaken for one another without anything being too badly misshapen.
2) Mutagenic chemicals. There are some substances which can leak into a cell and alter the copying process e.g. damaging the copying enzymes or causing the DNA strand to buckle and twist in the wrong way.
3) Natural decay. DNA isn't a robust chemical. In fact it's quite fragile. Parts of the strand will naturally decay, fall apart, ionise, bind to solvent etc. and give us unfamiliar structures, leading to new inaccurate copying.
4) Cosmic rays. Space is filled with small nuclei of elements flying at incredibly speeds. They zip around the galaxy, ionising molecules and initiating chemical reactions. Astronauts sometimes pick these things up with their eyeballs, seeing bright flashes appear in their vision. The source of these particles (cosmic rays) is unknown, but their effect is well documented. On Earth our magnetic atmosphere (magnetosphere) largely protects us from these rays, but one in every few thousand make it down to Earth. If they enter a cell, they can ionise it, meaning it will be mistaken for a different chemical and voila - more mutation.