Bitcoin transactions are not verified instantly – that would be a foolish (and near impossible) thing to do. Instead, they are verified in something called blocks. The network and protocol is set up so that users that do something called mining can find a block roughly every 10 minutes. Once the transaction is included in a (well, 1-6) solved block(s), the transaction is considered verified.
Miners are people who run bitcoin mining software on computer hardware. What this mining software does is a complicated process – but essentially it tries to perform a brute-force on a SHA-256 hash. The miner who finds a matching hash creates a block, and the miner is rewarded a certain amount of new bitcoin as a reward. It seems nuts, but they’re not trying to match for the whole hash, only parts of it – and that’s how the difficulty is adjusted over time.
It’s actually fairly straightforward – it’s just a fairly dynamic and slightly random process. Once a miner finds a block – that is they find a matching hash that creates a new block – they are given a reward for their efforts. This reward is hardcoded into bitcoin based on how many blocks have been created previously. As blocks will roughly be found every 10 minutes (the difficulty of the hash matching is adjusted every so many blocks to ensure this) bitcoin uses how many blocks have been made so far to determine the reward. The reward started at 50 BTC when bitcoin first came around in 2008, and will slowly half every 4 years until it reaches zero for a total of 21 million bitcoins in existance.
For this reason, bitcoin is considered a Deflationary Currency.