Asshur (Ashur) is the name of a northern Mesopotamian city state - one of three - which together are better known as Assyria.
A confederation of tribes, they initially settled on the coast of the Dead Sea, before being forced to emigrated to Egypt, only to return centuries later to form small kingdoms in Canaan during the period of deep social unrest around and after 1200 BC.
However, it doesn't necessarily have to refer to a wave of thirteen tribes and several hundred or more tribespeople wandering into Canaan.
Archaeology alone has disproved this version of events.
This has been deciphered as an origin for the name 'Hebrew' and a meaning suggesting the crossing of the Euphrates and the land beyond it, clearly a reference to the later Israelite migration westwards.
Eber is an ancestor figure of the Israelites and the Ishmaelites (Ishmael being a son of Abraham), as well as of the original Arabs in Islamic tradition.