A hash function is a function that take in an input of arbitrary length, and produces a fixed length output. Moreover, a hash function should be deterministic, meaning that the same input should always produce the same output. Also, we require that the output of a hash function should be uniformly distributed over its output space, meaning that every output should be equally likely given any input.
Intuitively, you can imagine the job for a hash function is to take some arbitrary data and produce a unique "identifier" or "fingerprint" for that data. Given that the output space is large enough (and some other conditions are met), we can use hash functions to do this. In effect, every bit of data we care to create an identifier for can be hashed to a unique output value. For instance, we may have a complete library of works of literature, and by hashing the contents of each book, we can create a unique identifier for each book. Common output spaces are 256-bits, meaning that we would have 2^256 possible outputs. To put this in perspective, the number of atoms in the observable universe is estimated to be around 10^80, which is around the magnitude of 2^256. For back of the envelope calculations, we can note that 2^10 is about 1000=10^3, so 2^256 is about 10^77, which is near the estimates of number of atoms in the observable universe.
SHA-2 is a family of hash functions that includes SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224, and SHA-512/256. The SHA-2 family of hash functions are widely used and are considered to be secure, though you should not hash secrets directly with SHA-2 (you can use SHA-3 instead). As with many cryptographic primitives, SHA-2 is standardized by NIST. It is used in many different protocols such as TLS, SSL, PGP, and SSH.
The hash function itself is based on the Merkle-Damgard construction, so it reads in blocks of data and processes them in a certain way. The output of the hash function is the hash of the data, which is a fixed length output. In our case, we will be using SHA-256, which produces a 256-bit output.
For more detail on the implementation of SHA-256 see this resource.
Also, you can find JavaScript code and a working applet for SHA-256 here.
Our implementation can be found in the src/hashes/sha256.rs file with detailed documentation and comments.