What is the word for a "journey planned by a group of people for a clear reason?"

A journey planned by a group of people for a clear reason is called an "expedition." Expeditions always have clear purposes, but the word is usually used to refer to journeys in pursuit of exploration, science, or war. For example, you can say that Vasco da Gama set out on an expedition to India in 1497. His purposes were clear: exploration and profit. Likewise, one often reads about the Carthaginian general Hannibal's expedition over the Alps and into Rome.

However--though technically accurate--not all journeys with clear purposes are referred to as expeditions. For example, you might travel from California to Maine to visit family members, but it would sound awkward to refer to it as an expedition (except as a tongue-in-cheek joke). Similarly, one does not usually speak of his "expedition" to the grocery store to buy eggs.