Logic family
In generic terms, a logic family is a group of logic devices which use common supply voltage(s), and common analog interfacing rules for their use in circuitry.
For example, in the TTL family, 'true' is normally a high (+5V) output, and 'false' is ground. (The meanings may be reversed when negative logic is in use, but the voltage levels remain.)
For a low output, a TTL chip will generally sink current into itself through the output pin (so that the signal direction is different at the logical and analog levels), send it to ground; for high output, it will source a small amount of current (at the 'high' voltage).
In commercial/marketing terms, a logic family is a line of compatible devices produced by particular manufacturer; e.g. the 74 series TTL family started life as a line of chips from Texas Instruments, before it became effectively a standard.