There is a small group of small ship cruiselines that advertise that they offer "expedition cruises". What do they mean by that?
Lindblad Expeditions probably says it best with their tagline "turning vacationers into explorers". An expedition is something an explorer would undertake. It suggests learning and discovery.
The destinations are generally more exotic than the rest of the small ship itineraries but not exclusively so. You can go on a pretty common itinerary and make it an expedition by deepening and enriching the experience.
You will find these same cruiselines mentioned in many of the geographic destination listings - gathering them here is just done to make them easy to see.
Lindblad Expeditions - is the grandfather of expedition cruiselines. They have partnered with National Geographic to create a series of cruises worthy of that institution. Their list of lecturers - historians, naturalists, and ecologists - reads like a scientific who's who.
Abercrombie & Kent - is known for all sorts of exotic and luxury trips. Their website even has a selection for "Extreme Adventures". In the small ship category their entries under expeditions are limited to Arctic and Antarctic cruises. While the orientation is adventure it is still done with standard A&K luxury.
Cruise North - emphasizes the Arctic with expeditions that make a powerful connection with the culture and land of Arctic countries.
Quark Expeditions - is really a polar specialist. They have 5 ships (including a nuclear powered ice breaker) that are continually involved sailing Arctic or Antarctic waters. Some of their ships offer near luxury accommodations while others are much simpler as befits an expedition ship.