When I hear the word carrier I think of like a baby carrier or a knapsack. To say the least, an aircraft carrier is somewhat larger than that.
As the name suggests, an aircraft carrier carries aircraft. As noted in the entry on aircraft, the word aircraft can be either singular or plural, but in the case of an aircraft carrier it’s almost always used as a plural. So we’re talking big. Very, very big.
Where do aircraft carriers carry aircraft? On the water.
If you want to transport aircraft over water—typically an ocean—but, for whatever reason, you don’t want to fly the plane over that body of water, a ship of some sort is a good bet because airplanes don’t usually do a good job of floating. Given enough time, most of them do a much better job of sinking when dropped on water.
Aircraft carriers do more than just carry aircraft. They also include a runway on their top level. The aircraft carried by the aircraft carrier can use this runway for takeoffs and landings.
Aircraft carriers are used for military purposes. Commercial airlines and private planes, on the other hand, use airports for planned takeoffs and landings. Their unplanned landings may occur anywhere, often with catastrophic results. But that’s getting well off the topic of aircraft carriers. Besides, you probably already knew all that.