Disc 2 is multiplayer: must and can only be installed. Disc 1 is the game: required for campaign and multiplayer. I installed it like I install every other game for load times and to ease strain on the drive, but not mandatory.
Sidenote: Disc 2 installs both War Games and Spartan Ops, both required to play their respective gametypes. However, there's pretty much dwindling, if not any support for Spartan Ops (since it was an "interesting experiment" to 343i), so to save yourself some HD space, I'd recommend you delete Spartan Ops after installing Disc 2.
This sig will self-destruct in 3.... 2.... 1.... Thank you for your time. Cookie? ^_^