An idea in your head is a fragile, ethereal thread.
It gets lost, permanently, without continuing active effort to hold onto it.
An idea in writing is an acorn: a durable seed that can stay dormant for extended periods of time, but can sprout in the future when the conditions are right.
Writing down an idea requires work, to transmute it from a fragile thread into a durable acorn.
But when you do it, you transmit the idea into the future with significantly less carrying cost.
Instead of the idea evaporating away when you get distracted, it stays as a viable self-contained package of information, with the possibility of sprouting in the future.