Unrouting a complete PCB in Eagle means that all routed tracks on the board are reverted back into so-called ‘airwires’. Airwires are lines that show that there is a connection between 2 points on the board, but that no actual connection is routed yet.
Unrouting signals on a board is called ‘ripup’ in Eagle slang.
When I do the layout of a PCB, in a first step I always do an auto-route of the board to check that the design can physically be routed.
Since I prefer to route sensitive signals and power lines manually, I always need to ‘un-route’ the board after the autoroute check.
To unroute (or ripup) a complete board, first activate the ripup tool by clicking this icon:
Then, click the ‘go’ button in the top of the Eagle window to ripup all signals: