The “cutting edge” of technology or craft is the newest / greatest stuff, pushing the field forward in new unexplored directions, by analogy to the cutting edge of a plow or a knife which slices through some uncut material or unbroken ground. I believe the metaphorical use of the term dates from the middle of the 20th century.

The “bleeding edge” is a more recent term for the same idea, emphasizing that being at the cutting edge might involve danger to yourself.