Application-Specific Integrated Circuit (ASIC) refers to computer equipment which are specialized for a specific use, rather than general use. An example of ASIC would be Bitcoin mining machines that are made to solve the SHA-256 algorithm repeatedly and in orders of magnitude quicker than general use hardwares (eg. graphic cards).
Initially developed only for the Bitcoin algorithm, the development, sale and usage of ASIC quickly became a lucrative industry as it expanded to cover many other cryptocurrencies.
It is worth noting that ASICs are not used only in the crypto scene - appliances that are made to do specific functions can also be equipped with ASIC chips for efficiency purposes.