means Full of substance — literally fleshy and protein-rich, or figuratively rich with content worth chewing over.

from From Old English 'mete,' which simply meant food of any kind, not specifically flesh — a hungry beggar's 'meat' could be bread. Over centuries the word narrowed to mean animal flesh specifically, and 'meaty' grew alongside it. The figurative sense — a 'meaty' role, a 'meaty' argument — leans on the same gut-level metaphor we find everywhere: substance is something you can sink your teeth into.