Avon means "river". "River Avon" in England therefore, literally means "River River" as does "Afon Afan" (River Afan) in Welsh.
There are several rivers named "Avon" around the world:
England
Wales
Scotland
Canada
New Zealand
Australia
The name "Avon" comes from the Welsh word afon meaning "river". (It appears that later arrivals to Britain would ask the indigenous people what the local river was called, and were told, in the local language, that it was a river). The etymology of Avon is the Proto-Celtic *abonā, meaning "river".