What do the numbers that represent the tire size mean?

Car dude is essentially right, except go to tirerack.com to see what all the other numbers mean (There can be a lot besides the basics in this example). A "Z" rated tire is actually for sustained speeds of 149+ miles an hour. This has nothing to do with how big a tire is. Since they jumped the gun and used the end of the alphabet early, two newer ratings have come into existance: W and Y. Y is currently the top sustained speed rating for passenger car tires, equal to 186+ mph. I guess they're reserving X for something really fast.

in your example the 225 is the width of the tire in mm ie how wide the tread is the next number, 50, a percentage. It means the sidewall of the tire is 50% of the width...ie 225x50%=112.5 mm and you are right about rim size. The letter shows the type of tire construction. R means radial. And if there is a number following the 17, it will provide speed rating. Z is common on tires this large meaning over 180 mph i believe

The 225 means that the tire is 225 Milimeters wide across the tread, the 50 means it is 50% as tall as it is wide.