when the wheel is on the car, there is a certain amount of space (clearance) between:
A) the wheel/tire's inside edge and the suspension (the spring/strut)
B) the wheel/tire's outside edge and the fender's inner edge
rims have a width and an offset. the width is self-explanatory; the offset measures where the mounting surface is in relation to the wheel's centerline.
when you change rim width, the clearance necessarily changes. for example, if you go from
6.5" wide rim w/ +45mm offset
to a
7.5" wide rim w/ +45mm offset
the clearance on each side of the wheel will change. in this example, since the offset is the same, the differnce in width will be split equally between each side of the mounting surface- therefore, the clearance between the suspension and wheel/tire will be 1/2" LESS, and so will the clearance between the outside of the wheel/tire and the fender.
for example, if you go 1" wider with, say, a 12mm difference in offset, the clearance on one side will be 1/4" less and on the other will be 3/4" less then w/ the OEM wheel.
by changing offset along with width, you can work to fit the wheel/tire by trading off clearance on one side for clearance on the other. the tire rack has a great page explaining the technical terms of wheel sizing.
i recommend reading that so you can understand what you're dealing with, especially if you're buying expensive wheels of questionable fitment.