I see the purpose of combat as two general tests, which can be done singly or in combination:
1. A test of the character/party's combat ability vs a single battle.
2. A test of the character/party's ability to endure a succession of battles.
Trash combat is when you have "passed" the current level of test, yet the game insists on making you retake it another 100 times before letting you graduate to the next level of tests. Given that I know the codex is almost entirely inhabited by geniuses, I'm sure everyone can relate to the time in school when you understood the material after about 5s of thinking yet the teacher droned on about it for hours. That's what Trash Combat is to me.
Of course, the "trashiness" of combat is highly dependent on other factors. I can accept a handful of weak, brief fights if needed for story purposes. But if your combat system does the JRPG 10s intro 20s spell casting animations 10s outro bullshit then fuck you and the horse you rode in on.
It's probably also worth discussing how certain games turn decent combat into trash combat. Namely, games like Dragon Age, NWN, and probably 99% of all AAA RPGs/JRPGs released in the last 5 years directly subvert test #2 by providing endless amounts of restoration items, infinite resting, or automatic healing after battle. If I go through a battle and absolutely nothing changes about my character other than my XP bar went up, the combat was irrelevant. As a contrast, take a game like System Shock 2 (not a conventional RPG, but bear with me as I'm replaying it at the moment so it sticks in my mind). SS2 resources are heavily limited and past the early game all combat will generally require some expenditure of resources, whether Ammo, Psi Points, or healing items. Due to this combat still has meaning no matter where or against what, because the act of combat will actually change the fundamental state of the player.