Leader refers to the fishing line from the weight to the hook. It is usually tied onto the end of the main line. It is usually thinner than the main line so fish cannot see it as easily. Depending on what type of fishing is being done and where it is being done, the leader is usually between 6 inches to 4 feet long.
In fly fishing, the leader refers to the line used from the end of the fly fishing line to the tippet.