AVR : Audio + Video processor + Receiver (radio)
It will have audio processing (and in some, video processing as Audiodoc has explained) and it will also have amplification part.
One may not need video capabilities of AVR if the TV has adeqauet HDMI inputs depending on the no. of sources.
Similarly a very good DVD/ BD player having 5.1 or 7.1 analogue outs can beconnected to simple 6 or 8 channnel amp for amplification
However AVR will be more convenient due to multiple features other than decoding like control with single remote, bass management, night mode,crossover settings etc.
It is said that AVR has to do too many things together and that's why may not perform as well as a dedicated amplifier if only amplification is considered.
There are some stereo amplifiers (like Harman kardon 3380/3490) which offer decoding but they are rare.