In developmental biology, and increasingly in evolutionary biology, one of the most important fields of study is deciphering the nature of regulatory networks of genes. Most people are familiar with the idea of a gene as stretch of DNA that encodes a protein in a sequence of As, Ts, Gs, and Cs, and that's still an important part of the story. Most people may also be comfortable with the idea that mutations are events that change the sequence of As, Ts, Gs, and Cs, which can lead to changes in the encoded protein, which then causes changes in the function of the protein. These are essential pieces in the story of evolution; we do accumulate variations in genes and gene products over time.
There's more to evolution than just that relatively straightforward pattern of change, however. Consider humans and chimpanzees. We're both made of mostly the same stuff: the keratin that makes up our hair and the organization of hair follicles is nearly identical, and our brains each contain the same structures. The differences are in regulation. We both have the same kinds of hair, but chimps have more of it turned on all over the place, while we've mostly down-regulated it everywhere except a few places. The differences in our brains may be mostly differences in select timing: our brains are switched on to grow for longer periods of time in development, and there are almost certainly specific regions and patterns of connectivity that are tweaked by adjusting different levels of different gene products in different places at different times.