The term “meaty” comes from the idea that good moves to lay on should strike deep into the opponent’s damage hitbox, and have a good number of active frames in order to make the strike inevitably hit or get blocked. Less popular terms like “deep hit” were also used with this intent. The term, hence, came to exemplify any striking habits good to lay on during the opponent’s wakeup (such as projectiles).
This term may be giving way to the Japanese term okizeme (“wakeup offense”; except that it is opposite to English “wakeup attack”), because it refers less to the exact kind of move to use and more to the fact that the wakeup game is one locus of option pressing, and is thus a more useful term in that regard. Perhaps I will switch this article over to that title at a time when this term is more prevalent?
Meaties ultimately come into play when you lay attacks right before your opponent finally finishes getting up. Right after scoring a forced knockdown, they are powerful because they are difficult to escape.
In fighting games, this is an extremely essential tactic for continuing offense.