To understand hash power in relation to Bitcoin mining we must understand what mining is (see here for in-depth understanding). In basic terms Bitcoin miners are racing to work out a target below a specific hashed input (which is the hash of a bitcoin block with an appended ‘nonce’) that is specially designed to be worked out every 10 minutes. This time frame is held constant due to the Bitcoin system changing difficulty to match the amount of hash power being pointed at it.
So hash power is the total amount of processing power miners are using (whether CPU, GPU or ASIC miners etc) to attempt to reverse engineer the hashed input. As we know, if the miner hashes the correct target, they receive a reward of Bitcoin.