Plain English Meaning
Pulling a small amount of fuel out of the lowest part of each tank and the fuel lines to check that it is clean, free of water, and the correct fuel.
Full Definition
The preflight act of draining a small sample of fuel from each fuel tank and fuel system drain point into a clear container, then visually checking the sample for water, sediment, or the wrong grade of fuel before flight.
Context Anchor
You encounter sumping during the preflight inspection, usually when checking each fuel tank drain and fuel system drain before engine start.
Derivation
From 'sump,' a low point or pit where liquid collects. In aviation, the sump is the lowest point of a fuel tank where water and sediment naturally settle, so 'sumping' literally means drawing fuel from that low point to inspect it.