The offset determines how far under the arch or how far towards the outer arch a wheel will sit. Each car has its optimum offset and a range within which the offset can be for the wheel to fit the car properly.
If the offset is too low for the range allowed, the wheel could stick out from the side of the car, if too high from what it
should be the wheel may catch on the suspension or bodywork as it will be too far under the car.
This is due to the fact that if you put a wheel on your hub with a higher offset than before, the wheels bolting face will have to move further under the car to meet the hub, in extreme cases causing the wheel to sit too far under.
If you take a wheel and cut it in half and draw a line down the centre of the width of the alloy wheel the offset will be the distance between the back face (mounting face) of the wheel and the centre line that you have just drawn.
The offset is commonly shown as the letters ET followed by a number, eg: ET49. The offset is always measured in mm and can normally be found stamped on the back of the wheel or behind the centre cap (if fitted).