Tippet is the piece of transparent line – usually monofilament or fluorocarbon – that is attached to the thin end of the leader in fly fishing.
The tippet is the final connection piece to the fly and has the lowest breaking strain of the whole set up.
Tippet is sized by diameter (the X system) and by breaking strain (lb test) – see this article for more on tippet sizing.
Tippet length varies according to the situation, but for a typical trout leader set up you might have a 10ft tapered leader going down to 3X with a two foot lenght of 4X tippet to give a 12 foot leader overall.