A graph showing some measure of the cost of performing some action against the number of times it has been performed. The term probably entered engineering via the aircraft industry in the 1930s, where it was used to describe plots showing the cost of making some particular design of aeroplane against the number of units made.
The term is also used in psychology to mean a graph showing some measure of something learned against the number of trials. The psychology graphs normally slope upward whereas the manufacturing ones normally slope downward but they are both usually steep to start with and then level out.
Marketroids often misuse the term to mean the amount of time it takes to learn to use something ("reduce the learning curve") or the ease of learning it ("easy learning curve"). The phrase "steep learning curve" is sometimes used incorrectly to mean "hard to learn" whereas of course it implies rapid learning.