SVD is a matrix factorization technique/a theorem of linear algebra that can be used whenever it is necessary to reduce the dimensionality of data and find latent features, like in a recommendation engine, for example.
SVD is a set of mathematical operations performed on a matrix, which outputs a series of other – lower dimension – matrices. The operations performed by SVD that decompose the matrix are three: an initial rotation, a scaling along the coordinate axes and a final rotation. These operations output three matrices (so that the product of these three matrices is equivalent to the initial matrix).
For further details and a far more accurate mathematical description, check the Wikipedia article about SVD.