ASIC stands for application specific integrated circuit -- they are used for all sorts of things, that require simple calculations, fast.

In the case of Bitcoin, they are basically the SHA-256 hashing algorithm implemented in hardware, rather than software. This makes ASICs faster than software being run on top of CPUs or GPUs. The downside is, that ASICs can do only one thing, and one thing only.

Note that cryptographic hashes are different from regular encryption -- they are neither symmetric or asymmetric, they are simply one-way cryptographic functions. That is, unlike symmetric or asymmetric encryption schemes there is no key that can be used to retrieve the original data.