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 used to teach design. Before a presentation, I always asked my student to explain their project to someone with no knowledge on the subject, like their grandmother or so. Mainly to discover the logic flaws in their presentation.