The wheel offset is the distance from the hub mounting surface to the centerline of the wheel.    The diagram shows a positive offset in which the mounting surface is outside of the wheel centreline.  This suspension/ wheel combination was chosen to maximize performance.  You can see that the suspension geometry intersects the centreline at the road surface for optimal handling.

 Scrub Radius

 Selecting A Lower Offset

If you select an aftermarket wheel with the exact same offset, you will always have the exact same scrub radius.  Suspension and handling properties will not change.

If the new wheel is wider than the stock wheel, you will loose clearance on both suspension and wheel well sides.  There is obviously a limit to how much of a width change you can make.

Often a driver will select a wheel with a smaller offset than stock.  This diagram shows a zero offset where the mounting surface is equal to the wheel centre.  (You could go even farther and select a wheel with a negative offset.) 

A smaller offset will create a scrub radius which may affect the handling of the car, but there are a number of reasons why you may need to choose a smaller offset.

1. To compensate for a wider wheel:  A wider wheel with the exact same scrub radius as the stock wheel will be positioned closer to the suspension components.  If the wheel is too much wider, it will not fit.  To compensate, you would choose a smaller offset to move the wheel away from the suspension.

2.  To create a wider stance:  By setting the wheels outward, the stance of the car becomes wider and stability  is increased.  In some applications, the benefits of this stability are greater than the drawbacks of the scrub radius change and the driver may make this compromise.

3.  Looks:  A smaller offset moves the wheels outward, so they have a tendency to fill out the wheel well better.  Cars set up for show, more than performance will often choose a lower offset wheel, however, if the offset is too small the sidewall will rub the inside of the fender.