Correct fitment of tires and wheels is of essential importance. Improper combination of tires and wheels lead to incorrect speedometer display, increased fuel consumption and decreased stability of the vehicle.
Wheel sizes are expressed as WW x DD sizes. For example 6 x 14. A 6 x 14 wheel is has a rim width of 6 inches, and a rim diameter of 14 inches. The width is usually below the width of the tire for a good match. So a 185mm tire would usually be matched to a wheel which is 6 inches wide. (185mm is more like 7 inches, but that's across the entire tire width, not the bead area where the tire fits the rim.)
The important thing that you need to keep in consideration is rolling radius. This is the distance in mm from the center of the wheel to the edge of the tread when it's unladen. If this changes because you've mismatched your new wheels and tires, then your speedometer will lose accuracy and the fuel consumption might go up. The latter reason is because the manufacturer built the engine/gearbox combo for a specific rolling radius.
Styling and performance are the only two reasons. Most cars come with narrow little tires and 13 inch rims. More recently the manufacturers have started putting decent combinations on factory cars so that's not so much of a problem any more. The first reason is performance and more specifically stability in corners at high speed. If you have larger rims, you get smaller sidewalls on the tires. And if you have smaller sidewalls, the tire deforms less under the immense sideways forces involved in cornering, thus making the car more stable.
The plus one concept easily describes the proper sizing up of a wheel and tire combination. Basically, each time you add 1 inch to the wheel diameter, add 20mm to the tire width and subtract 10% from the aspect ratio. This compensates for the increases in rim width that generally accompany increases in diameter too. By using a larger diameter wheel with a lower profile tire it's possible to properly maintain the overall rolling radius, keeping odometer and speedometer changes negligible. By using a tire with a shorter sidewall, you gain quickness in steering response and better lateral stability. The visual appeal is obvious.
