Podcast is a portmanteau of iPod and broadcast.
The word iPod was inspired by the EVA Pods from 2001: A Space Odyssey, where an iPod functions as a companion to a personal computer much like a pod is a companion to a larger spacecraft.
The word pod when used in relation to spacecraft is inspired by pods containing seeds like peas.
Broadcast comes from the words broad and cast, where broadcast is to sow seeds by scattering them.
So by pure coincidence, both parts of podcast are related to seeds.