Programmers often discover solutions while explaining a problem to someone else, even to people with no programming knowledge. Describing the code, and comparing to what it actually does, exposes inconsistencies. Explaining a subject also forces the programmer to look at it from new perspectives and can provide a deeper understanding.
I write a lot of notes, because I can’t trust myself to remember details of any project after a day or more of hopping through multiple other tasks and online information onslaught. This particularly concerns any problems on which I get stuck — and whaddayaknow, writing out what specifically doesn’t work and how it should work, helps with realizing why it might not work.