What is the difference between a HMAC and a hash of data? On a recent question it became apparent that there's a significant difference between an HMAC of input data and a hash of input data. 

What exactly is the difference between an HMAC and a hash of a span of input data?
TL;DR, an HMAC is a keyed hash of data.

A good cryptographic hash function provides one important property: collision resistance. It should be impractical to find two messages that result in the same digest.

An HMAC also provides collision resistance. But it also provides unforgeability. In order to generate an HMAC, one requires a key. If you only share this key with trusted parties, given an HMAC signature, you can be confident that only one of the trusted parties could have generated that signature.

Due to common properties of hash functions, an HMAC is not as simple as hashing the data appended to the key. This construct is vulnerable to length-extension attacks where an attacker can take a message and its HMAC signature, and use this to construct a longer message with a valid signature (thus breaking the guarantee of unforgeability).