The leader in fly fishing is the transparent section of line that joins the opaque fly line to the tippet. Leaders in fly fishing are typically between 7 and 15 feet in length (roughly between two and four metres).
Most leaders are tapered in that they have a thicker section towards the butt and get progressively thinner at the tippet end.
The leader is a vital connection between the angler and the fish (once it has taken the fly). Leaders are rated by their strength based on the breaking strain of the weakest part of the leader (near the tippet).
Leaders are rated in terms of pounds (or kilos) referring to the breaking strain of this section. They can also be rated using the “X” system, which is another way of delineating leader strength (see here for more detail).
Leaders are also rated by stiffness. This mainly refers to the butt section and how stiff this section is determines the casting characteristics. A stiff leader is good if you are fishing a really long leader or in heavy winds, as the stiff butt will help it turn over. A more flexible butt section is good to delicate casts where you need to present your fly gently usually when dry fly fishing.