As we develop, there are changes in gene expression. Things get stuck on DNA sequences (methyl groups, at least one kind of RNA) - and there are other things that get attached to the histone "tails" (histone groups are kind of a spool the DNA is wrapped around) that either enhance or reduce expression. These changes are important for tissue development (both a brain cell and a muscle cell have the same DNA) - but they continue after we're born, and is a major reason identical twins become more different from each other as they get older.

FWIW, this whole process is labeled 'epigenetics' (which just means along with genetics), and if you're looking for an introduction, check out the books authored by Nessa Carey.

Disclaimer: non bio guy here, got sucked into this through a fascination with evolutionary developmental biology (AKA evo-devo).