Chris, you mentioned you weren't sure how the difficulty of Halo single-player scaled. (For instance, whether it was simply damage numbers being increased or whether it was something more)
One of the game designers for Halo did a great GDC talk on the design of halo games that he worked on throughout the series, specifically the balancing for the multi-player and single-player of the game.
It's probably my favorite GDC talk. Jaime dives pretty deep in some of the reasoning for decisions, and goes into psychology and even a bit of philosophy:
Session Name: Design in Detail: Changing the Time Between Shots for the Sniper Rifle from 0.5 to 0.7 Seconds for Halo 3
Speaker: Jaime Griesemer
The title may seem a bit strange/oddly-specific, but it's for a good reason. Take a look if you haven't seen it already.
To answer the question though, they do quite a few things; increasing the aggressiveness of enemies, increasing the number of enemies and the level of the enemies. They also do more clever things like such as increasing the speed of non hit-scan projectiles like that of the ubiquitous plasma pistol. This makes them harder to dodge and forces the player to stay closer to cover on higher difficulties.