Zak Smith once make the analogy to me that D&D campaigns are similar, in one way, to rocket flights. If you can reach a certain amount of orbital velocity (player buy-in and enthusiasm), the campaign can just keep going forever on pure momentum as the players achieve goals and pick new ones. But boosting up to that level of investment takes a lot of energy, and you have to "do something" during that time to keep players engaged and events moving along. In the case of standard D&D, the "boost phase" of a campaign is when you're exploring dungeons, killing monsters, and collecting loot. They provide short-term goals while the deeper story is developed.
Another analogy I think works is how good television shows may start with a "monster of the week" format, but as recurring heroes, villains, and sub-plots become developed, the show can mature to a longer, more character driven, and much more satisfying long-arc format. Shows from my youth that made this transition include Deep Space Nine, Buffy the Vampire Slayer, and Babylon 5. To bring this back to D&D, campaigns start with a "dungeon of the week", and then ideally mature into something better.
However, that's for standard D&D. I want to develop a one-line description of the most common boost phase of various popular campaign worlds. Here are my attempts, but please feel free to chime in with refinements and improvements:
Standard D&D. Collect rumors on monster activity, explore dungeons, old keeps, etc.; kill monsters; take their stuff.
Ravenloft. Investigate rumors of villages or families disturbed by paranormal enemies; try to find ways to discourage the enemies from bothering them further, or find an escape plan to safety. Direct confrontation is rarely a wise course of action.
Spelljammer. Get a ship, get a crew, find a job, keep flying. Wait, no, that's Firefly. Get a ship, go explore abandoned hulks and meteor fields for salvage. [I had a post on my old blog, which I stupidly deleted, about how Spelljammer needs rules for super-cheap and crappy ships that PCs can start with]
Dragonlance. [Note that I'm assuming general campaign play, not one of the core adventure paths]
Dark Sun. Try to survive while avoiding the Templar's police. A lot like D&D, except the "treasure" is often water and food resources.
Planescape. Learn the cant, bang around bad neighborhoods, take jobs that send you to the burgs and safer planes.
Al-Qadim. Assemble a caravan, head for another city to trade. Inevitably get way-laid by some form of genie, who makes life interesting. Roll on the Random Pissed Off Djinn table. Sorry guys, you're all cursed until you retrieve the Lost Diadem of Sultaness Sul'Kira ma Dar of the El Dynasty.