There are so many different bicycle tires selecting them can be overwhelming. The first thing you want to get right is the diameter. For a road bike this is mostly 700c or 650c, and for a mountain bike 26", 27.5", or 29". Next is the width with road tire ranges from 20mm-30mm. It is important to note that many road bike racing frames will not accommodate a tire wider than 28mm. The current size of your tire will be stamped on the sidewall.
Beyond size, bicycle tires are designed for traction (including in the wet), puncture resistance, or low rolling resistance and speed- usually a mix of these criteria. The "TPI" is often listed as well which is the "threads per inch." Generally speaking a higher TPI improves ride quality and puncture resistance but that is not a certainty.