A subgroup of the nodes of the Ethereum Classic blockchain are miners. These miners group transactions in batches, add to them a time stamp, the previous block cryptographic stamp or hash, and a random iterating number called a nonce.
Once they do this, they create a new cryptographic stamp for this new block specifically and immediately check if it hit a specific target that the protocol determines. If it didn’t hit the target, then the miners go back, change the random iterating number as soon as possible and try again. If they didn’t hit the target again, then they try again, and again, and again, until one of the miners hits the target.
They may do this trillions of times per second, and this is what uses up so much energy and is referred to as “proof of work” because only by working in trying so many times, using so much computing power and electricity, is that, statistically, one of the miners will hit the target within the range of the standard block time, which is 13 seconds in ETC.
When a miner hits the target, then they send the block to the rest of the network for verification and payment of the miner reward plus the block's transaction fees.