Pairing-based cryptography uses bilinear maps to create a gap group that allows efficient constructions of certain primitives.
Pairing-based cryptography (PBC) uses bilinear maps (typically on elliptic curves) to create a group where the DDH assumption is easy while CDH and DL remains hard: a "gap" group.
Among the applications of PBC are different functional cryptography such as identity-based encryption and attribute-based encryption, short signatures, verifiable random functions, and non-interactive zero knowledge proofs.