When regarding the motion of an airplane or a ship, what exactly is "yaw"? Is it quite different from pitch and roll?

Yaw can be dangerous, as the diagram shows. When you have two engines, and one fails, you yaw. The equivalent in a car would be skidding down the road while the car is aimed to the side. When the wheels engage, you lose. In yaw, the unpowered wing can stall and you drop like a rock, but in a helix; that's pitch and roll. Yaw is why the tails of planes are as big as they are. The rudder must be big enough to handle yaw from engine failure or cross winds. It took 50 years of computer fly-by-wire technology to solve the yaw problem for tailless planes. But all planes with tails commonly fly while yawing. Whenever there is a crosswind, the nose of a plane is not pointed in the direction it is travelling with respect to the ground.
BTW, elevators in the tail (the horizontal part) control pitch and flaps in the wings control roll.

The "Yaw" movement is achieved by pushing the right or left rudder of the airplane. Normally it is used in conjunction with the yoke or a stick in certain airplanes which controls the elevator (nose up and down) and ailerons ( roll right or left) In a co-ordinated turn, the pilot applies yaw movement on the relevant pedal and applies back or forward pressure on the elevator (depending on the type of turn and power and prop settings). During a take off run in a single engine airplane, the pilot applies right rudder in order to counter the P-Factor -- the uneven thrust resulting from the ascending and decening blades and Slipstream Factor which tend to cause the airplane to yaw to the opposite direction of engine rotation (like a big gyro). The same happends in landings when the ground effect (air cushion resulting from air "bouncing" from the wings to the ground artifically reduces the induced drag.