Why does DNA mutate?
If I am not mistaken, the vast majority of mutations happen during DNA replication.

DNA must replicate itself so that cells can replicate itself. The DNA polymerase is one very important protein that replicates DNA. The human genome (to consider this example) is 3.5 billions nucleotides long. Just to realize how long is 3.5 billions letters, let's make a book analogy.

Book analogy


In the Harry Potter series, there are about one million words (ref).
In the LOTR series, there are about one 400 thousands words (ref).
In the Chronicles of Narnia series, there are about 230 thousands words (ref)
In the King James Bible, there are about 788 thousands words (ref)


This sums to about 2.4 millions words. As, in english, there are 5.1 letters on average per word (ref), this lead to a total of about 12.3 millions letters. Imagine you have to rewrite all of these books almost 300 times (12.3 millions * 300 ≈ 3.5 billions)! How many typos would you make? 

There are several cell divisions between a zygote and the ovule/spermatozoid produced by this individual but as most mutations happen during meiosis, I will just ignore mitotic mutations. The DNA polymerase makes about one typo every 100 millions nucleotides (Kong et al. 2012; Rahbari et al. 2016)! So really, the DNA polymerase is doing a pretty good job!

What is causing mutations?

Shit happens

I am hoping that form the above analogy, you may have a sense that mutations are just small mistakes. They happen because the replicating machinery is not perfect. Sometimes a molecule comes sideway, does not bind very well and another molecular passing by sticks to the DNA, etc.. Errors happen just like you would be making a lot of typos, rewriting books.

Mutagens

There are of course factors that can affect this mutation rate. Physical, chemical and biological agents increasing the mutation rate are called mutagens and they include radiation decay, ultraviolet radiation, ROS, benzene as well as some viruses and some parasitic bacteria.

Variation along the genome

Note also that the mutation vary along the genome too. Regions with high repeats (e.g. AATAATAATAATAATAATAATAAT) such as microsatellites for example tend to have a much higher mutation rate.

Variation among species and Drake's rule

Mutation rate also vary among species. There is a general tendency that the per nucleotide mutation rate negatively covary with the genome size, a phenomenon called Drake's rule (see for example Bradwell et al. 2013 or one of the early Drake's paper).