Basically it's a stand alone IC (integrated circuit) or grp of IC's that perform a programmed task repeatedly. It's a bit like the controllers and circuits running a washing machine or tv, except in this case, their sole purpose is to act like calculators doing very specific calculations.
They can run on their own or slaved together to tick away doing the calculations.
The purpose of those calculations is to solve the functions that enable the generation of a bit coin - essentially instead of people using their own desktop pc as a bit coin miner, these stand alone units are built to efficiently do that one task.
When I say stand alone - by that I mean not an application on your pc - the miners will have to be connected to the internet as they use peer to peer networking to verify the work they have done and receive the rewards for that work.
Essentially - a mathematical problem requiring X amount of processing power to solve will generate Y number of bit coins.
When enough calculations are done and the particular problem is solved - Y number of coins will be distributed to those that solved it.
The calculations don't achieve anything and are worthless except for the fact that by doing them, bit coins are rewarded.
If you are really stuck with the subject or enough people struggle to understand what bit coins, mining and AISC's are I might be able to write a noddy guide if needed.
I don't have anything to do with bitcoins or bitmining myself, but I have a reasonable understanding of the principles and practice.