So, I attacked the Orc capital on a random map last night. I had 3 stacks to the AI's 3 stacks. It was hard fought but I won the battle. I killed the leader with a couple of Halfling rogues and a well-timed Magic Fist.

When the battle was over I expected the city to flip to my control but that didn't happen. There were still two Orc armies showing on the strategic map, despite me wiping all the Orcs out (or so I thought). I hit next turn (Classic mode) and when I get control back I find that the enemy leader has respawned and seems to have plenty of troops.

What am I missing here? Why did I not take the Orc capital after my successful battle? Did I actually need to move one of my stacks into the center-city hex on the strategic map?

Any help appreciated - I really like this game but don't always understand it...

Yes, you need to reach the central tile of a town in order to capture it. Slain wizards automatically respawn the next turn as long as they still possess at least one wizard tower.
Regular units, however, are not so lucky... once they're dead they're dead (necromancy permitting) so I'm not sure where all those additional troops come from, unless they were already nearby.

OK, I kind of figured it was that I didn't move into the "tower hex" so to speak. Unfortunately I had no movement points left on my stacks - I will plan differently next time.

The other enemy stacks - It is entirely possible that they were just under the fog of war/unexplored area and came into the city hexes when I hit "end turn." If the AI Leader hadn't respawned on that same turn I probably could have beaten them. I had taken a couple casualties but nothing major.

Taking an AI controlled Capital when it hoards units can be super annoying. Once you start winning a map, the AI will put five or six full stacks in their capital. Not much fun. It does make for some epic turns when your three stacks have to assault a city with three stacks twice in one turn.

Re: Movement - I'm sure you know this, but you can use just one unit from your three stacks of 24 total units to initiate combat. That way your Slingers or Catapults won't stop the assault.

Actually, I did not know that... Rather, I should say that it never occurred to me but of course it would work that way.

Thanks for the tip!

You can use this in other instances than city assault as well. Ie. you can only move your army next to structure you wnat to capture, send only the fastest unit there, everyone will join the fight and you will save some movement. Then you can move away with everyone.