Bacteria reproduce through binary fission. Each time this happens, there is a certain chance that a mutation will occur. This is measured through mutation rates. Generally, these rates are low. However, bacteria not only live short lives, but they also reproduce extremely fast. Thus, due to the high reproduction rates, mutations can accumulate rapidly in a population.
It is similar to the process of making a copy of a copy. However, there is some dirt on the xerox's plate. Thus, the copy will have these spots. Now, if you make a copy of a copy, this second copy will have double the amount of spots (mistakes) than the original. Now image this proces going on and on and on.
Not all the copies will survive, as not all mutations are beneficial (the process of natural selection). However, even if a small percentage survive (have advantageous mutations) and the copying process (binary fission) occurs fast enough, mutations will accumulate quickly. This will lead to a quick evolutionary process.