The particular hash function that Bitcoin chooses to use in many scenarios is called SHA-256.
SHA-256 is a cryptographic hash function that was designed by the NSA.
SHA-256 is a member of the SHA-2 family of cryptographic hash functions, SHA standing for Secure Hash Algorithm.
SHA-256 takes in an input of size less than 2^64 bits and produces a 256 bit fixed size output.
In practice, the 2^64 bit upper bound on the input size is so massive that we usually just say that it takes in an arbitrary amount of information.
Bitcoin, in many cases, uses SHA-256 squared, or SHA256d, which simply means that SHA-256 is used twice in a row.
Once on the original message you want to hash, and another time on the output of this first hash.