What is a hash rate?
A hash is the output of a hash function, and in the context of Bitcoin, the hash rate is the rate at which a computer completes an operation in Bitcoin code. A higher hash rate is better for mining, as it increases the chance of finding the next block and receiving the reward.
Hash rates when mining
Hash functions are deterministic and the same input always produces the same output, but they are designed to be unpredictable.
To mine bitcoins, miners must find an input that contains a list of all recent transactions that need to be verified and whose hash is less than a certain value. (This value is adjusted regularly to change the difficulty.)
As soon as a miner finds such a value, he sends it out. The number of transactions he has included is now verified, and this sentence becomes the next block in the Bitcoin blockchain. The miner then receives a reward for providing his computing power to operate the Bitcoin protocol.
Since the only way to find such value and get the reward is to use a brute force search, ever faster hardware has been developed to quickly calculate the SHA256 hash function. The hash rate indicates how often this function can be calculated per second.
Some computers can now calculate trillions of these hashes every second.