Many factors affect launch angle, including swing speed, angle of attack (how the clubface approaches the golf ball) and clubface position at impact. The loft of the golf club itself is the single biggest factor, of course. But the same club can produce very different launch angles in the hands of different golfers based on the other factors. A club will produce a higher launch angle with a higher clubhead speed, for instance, so long as other factors are equal.
Launch angle is a term probably most closely associated by most golfers with drivers. The advent of oversized, game-improvement drivers in the late 1990s, and then the greater availability to the average golfer of clubfitting tools such as launch monitors, have increased the focus on launch angle. If a manufacturer can tweak a driver's clubhead design - factors such as loft angle, center of gravity location and moment of intertia - and tinker with the club's overall weight and aerodynamic design in a quest to boost swing speed, then the manufacturer can help improve a golfer's launch angle off the driver.
And an improved driver launch angle often means more carry, which in turn leads to more distance.
Launch angle does factor in with all golf clubs, however, and it should be noted that a higher launch angle is not always the preferred outcome (particularly moving through the set to the wedges).
But to restate the basic definition: The launch angle is the ball's angle of ascent relative to the flat groundline.