Supergravity was first formulated as a four dimensional theory in 1976. Very quickly, it was extended to higher dimensionality. It is a theory of elementary particles based on supersymmetry, the Super part, and Gravity, in the form of General Relativity. This means that it is a local symmetry rather than a global symmetry. It was the first theory to bring together all four fundamental forces; the electromagnetic force, the weak nuclear force, the strong nuclear force and gravity.
While General Relativity describes gravity on a large scale, it breaks down at very short distances. Supergravity describes gravity as a force carried by a boson called the Graviton. Unlike the other bosons that have spin "1", the graviton has spin "2". All bosons have integer spin, unlike fermions that have half-integer spin, for example, "½", "1½" etc. Unfortunately, supersymmetry requires every particle, fermionic and bosonic, to have a new supersymmetric "partner" as described in the preceding section. The supersymmetric partner to the spin "2" graviton is the spin "3/2" gravitino. An upside of Supergravity is that it avoids the infinities inherent in most other quantum gravity theories. A downside is that when Supergravity models are reduced to four dimensions, the cosmological constant becomes excessively large, and the model must be fine-tuned.
Interestingly, having fallen somewhat out of favor when Superstrings came along, certain 10-dimensional Supergravity theories are now considered to be the low energy limits of string theory, and 11-dimensional Supergravity is considered to be the low energy limit of "M" Theory. Research continues on Supergravity both in terms of string and "M" theory and in its own right, because Supergravity does not require string or "M" theory as its high energy limit; it could be that a completely different theory comes into play.
Here is a somewhat technical introduction to Supergravity from Wikipedia.