In simplest terms, cryptomining is using your computer (mostly graphics card/s) to help create a ledger of every transaction of virtual money (crypto currency).
The ledger (or blockchain) is a highly encrypted record that must be added to every time a bit of the currency changes hands or is created, and graphic cards are usually well suited to do these kind of calculations. This work is done by "miners" and it's important work as it keeps an accurate record of where every coin is and how it came to be.....so that it can't be counterfeited. The reward for the miners is they get to create new coins (for themselves) by doing this work. The bigger the chain becomes the harder it is to add to as the whole chain needs to be updated, this helps drive up the value of the currency as it becomes harder and harder to mine the next coin.
Anyone with a computer can become a miner, all you need is the software and membership to an online mining pool.
The reason it's bad for the GPU business, well it's not bad for the manufactures (NVidia and AMD) as their products are selling for way more than they should. It's only bad for the average computer gamer who wants a graphics card as the prices are way too high because the miners are buying just about everything they can.....simple supply and demand, the demand is higher than the supply, so the price goes up.