Explanation...
OK, here goes the full explanation. Let me know if you need any further clarification.
Tires are classified by size. Stock you said was 235/75 R15. The 235 is the width of the tire in milimeters. Divide by 25.4 and you'll get the width in inches, in this case 9.25 inches. The 75 refers to the height of the sidewall as a percent of the tire's width. So if the tire is 235mm wide, then the sidewall is 235mm x 0.75. That would be 176.25mm. In inches that would be 176.25/25.4 or 6.94 inches.
Now, to find out what tires will fit, you need to find out the diameter of the tire. For any tire it will be twice the sidewall plus the rim size. So for the stock Explorer tires, it's (6.94 x 2) + 15. That would equal 28.9 inches. Any tire/rim combo you get should preferrablybe plus or minus 0.2 inches from the stock size, or your speedo will be out of whack. For the Explorer that would be 28.7 to 29.1 inches.
To figure out what size you can use for an 18" rim, just work backwards. Take the diameter (28.9) and subtract the rim size (18). That leaves 10.9 inches. The 10.9 is the size of both sidewalls together, so divide by two. That gives a sidewall height of 5.45 inches. Now just check and see what size 18" tire will give a 5.45" sidewall. Let's use leejen's example of 285/50 18.
Tire width of 285mm times 0.5 is 142.5mm. In inches that is 5.6 inches. Should be close enough. Add it all up and you get a diameter of 29.2, which should still be OK.
Sorry this reply is so long. As leenjen said, just go use the wheel wizard. But at least now you know what the numbers mean. Oh, by the way, when speaking of tires/wheels, any combo that is approximately the same diameter as stock, but has a rim one inch larger, it's called +1. If the rim is two inches larger with same overall diameter, it's +2. I think you get the idea.
Any other questions you have feel free to ask. Hope this helps.