The "120" is the nominal width of the tire, in millimeters.
The "80" is the aspect ratio, expressed as a percentage of the width.
The "V" is the speed rating for the tire.
The "16" is the diameter of the wheel that the tire is constructed for.
The nominal width is approximately how wide the tire is at the widest part of the tread. In this case, the width is about 120 mm. There is some variance from tire maker to tire maker, and from brand to brand, so one tire may be 124 mm wide, while another may be 118 mm.
The aspect ratio is approximately how tall the tire is in relationship to its width. Thus, a 120/80 tire is about 95 mm tall, from the bead to the tread surface.
The speed rating indicates at what maximum speed the tire is considered safe for continuous use. In this instance, the V stand for speeds up to 149 mph. A table of speed ratings is listed below.
The last number is the diameter of the wheel that the tire is intended for. In this case, we are talking about a 16-inch rim for the tire.