What is 'provably fair' in Bitcoin gambling?

Could you elaborate on the concept of 'provably fair' in the context of Bitcoin gambling? I've heard this term but am unclear about its exact definition and how it ensures transparency and fairness in Bitcoin-based gambling platforms. Specifically, how does the process work? Does it involve cryptographic hashes or other verification methods? What steps should a player take to verify that a game is indeed provably fair? And finally, how does this concept contribute to the overall trustworthiness of Bitcoin gambling sites?