Basically it is the distance between the centre of the rim and the hub. If you change it significantly enough you will find it changes the handling characteristics of the vehicle.
+38 offset extends the outside of your rim by 3.8cm compared to stock. Reduces inner clearance by 2mm.
A good compromise for an 8" rim would be a +45 offset. You don't want to go too high an offset with such a wide rim or it will reduce clearance to the caliper and strut by too much. So the wider the rim - go with a lower offset than stock (but not too low).
Play around with this calculator and you will see how it works. In your case I think you got bad advice about which were suitable rims for your car. Some tyre shops focus too much on whether rims will "fit" as opposed to whether they are suitable.
http://www.1010tires.com/WheelOffsetCalculator.asp
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