A fixed-wing aircraft is one who's wings are fixed.

I suppose you want a more in-depth explanation than that.

On aircraft, the devices that produce lift are called "wings." They are constructed so that as they pass through the air, they creat lift. More detail can be found in the wing node. They pass through the air by being pushed there on an aircraft, by the aircraft's engine - but what pulls the aircraft forward, exactly?

Why, the propellor of course. The propeller is also a wing. It passes through the air by the spinning motion of the engine, and creates lift - also, because it powers the aircraft, it is known as thrust.

The Propeller is not a fixed-wing. It is not fixed. It spins.

The wing on the aircraft is a fixed-wing. It is attached to the aircraft and does not move.

Any aircraft where the main lift-producing device (wings) are attached and do not move, are referred to as fixed-wing aircraft.

Aircraft where the main lift-producing device (wings) are NOT attached and DO move, they are referred to as ROTARY-wing aircraft. This would include Helicopters.

Note that aircraft which have slightly moving wings (some high-speed fighters and bombers for example) are called swept-wing aircraft, and are considered fixed-wing.
As an addendum to weasello's excellent writeup above, and for contrast, I offer the following list of aircraft classes as they are (or soon will be) recognized by the U.S. FAA:

Note that aircraft must be certified to be flown in the U.S., with the exception of experimental aircraft. Recognizing the continuing debt owed to the garage tinkerer by general aviation (and, by extension, everything up to and including the Space Shuttle - thanks Orville and Wilbur!) the FAA allows homebuilt and even home designed airplanes restricted use of the nation's airspace. The tradition of experimental aircraft designs flown by their inventors is going strong - see Bert Rutan for an example.

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