Aspect Ratio is the ratio of the drill diameter to the thickness of the intended copper plated structure.
The ratio gives an indication of the chemical processes ability to provide copper plated holes.
Put simply, if your PCB is 1.0mm thick and you drill a hole through it of 0.5mm, then the Aspect Ratio is 2:1.
ie: PCB Thickness divided by the drill diameter. 1.0 / 0.5 = 2