A size 16 tire is one that fits on a wheel that is 16 inches in diameter. That measurement is part of the coding found stamped on a tire sidewall. Other items in the code indicate tire type, width, aspect ratio, construction, load index and speed rating.
Using the stamp "P 195/65R15 95H" as an example, the P stands for passenger vehicle, and the 195 is the tire width, measured in millimeters from sidewall to sidewall. The 65 is the aspect ratio, or the ratio of the tire height to its width. The R stands for radial construction, and 15 is the wheel diameter. The 95 is the load index, or how much weight the tire can support, while H indicates that the tire can handle speeds up to 130 miles per hour.