On the 24th-century warp scale, the theoretical threshold of infinite velocity at which a ship occupies every point in the universe at once, crossed by Tom Paris in an experimental shuttle in 2372.
Warp 10 is the upper limit of the warp scale used in the 24th century. It is not simply a high speed but infinite velocity: an object travelling at warp 10 would be everywhere in the universe simultaneously. Earlier scales were different, which is why ships of Kirk's era could quote warp factors above ten.
In the Voyager episode Threshold, Tom Paris, B'Elanna Torres and Harry Kim use a newly found form of dilithium to push the shuttlecraft Cochrane across the barrier. Paris succeeds and returns with sensor records of an enormous volume of space.
The flight has a price. Paris begins to mutate rapidly, abducts Captain Janeway and takes her on a second warp 10 flight, and both are found on a jungle planet transformed into amphibian creatures before the Doctor restores them.