Latency normally describes the time that a signal or data packet needs to pass from one part of the signal chain or network to another. It is a certain 'time' respectively it is a certain 'delay'. This could be the time an audio signal needs to pass a circuitry of an entire device from input to output. It also could be the time needed for a data packet to get from one designated point to another one.
Propagation delay is the travel time at speed of light respectively the time it needs to travel in the medium (sometimes lower than speed of light). Propagation delay is calculated by distance divided by the travelling speed in the medium.
Transmission delay is the time that is needed to carry all the individual parts (bits) of a packet on its way, therefore it is a function of the packet's length.
The latency of a certain device is the sum of all delays involved in the transmission of the signal. These are the propagation delay of the signal itself, the transmission delays within the device, processing and eventually even storage delays.
The usual latency of audio processing devices are between 1 and 30 milliseconds. Digital video processing units normally have a latency of at least one but often several video frames.