Mining is done through an ongoing series of rounds to create and add new blocks to the blockchain. This process serves as the engine that confirms and archives all transactions on the Burstcoin network. Its continued operation is of vital importance to the utility of Burstcoin, which is why miners are continually rewarded by participating in this system.
When a round starts, all miners begin scanning their hard drives attempting to find the best solution for that round, also known as a deadline. The miner who has found the best (shortest) deadline for that round is then able to forge the next block on the blockchain and so that miner wins the reward of Burstcoins for that round. A miner's chance of forging a block at any given time is based on that miner's plotted capacity relative to the plotted capacity of all other miners on the network (network difficulty).
The details are much more complicated and I encourage you to explore those further, but that summarizes the basic concept.