In cryptography, a one-way compression function is a function that transforms a fixed-length input into a fixed-length output.
The transformation is "one-way", meaning that it is difficult given a particular output to compute inputs which compress to that output. One-way compression functions are not related to data compression, which by definition is invertible.
A compression function mixes two fixed length inputs and produces a single fixed length output of the same size as one of the inputs. This can also be seen as that the compression function transforms one large fixed-length input into a shorter, fixed-length output. That's how, for example, hash functions can be produced from the Block Ciphers.
See also: Trapdoor function (it's not so related as it might seem at first).