The main component of a bicycle is the frame, onto which the wheels and the other components of the bicycle are mounted. The frame design that is the most common in today’s biking community consists of two triangles—the main triangle in front and a paired triangle at the rear.
The frame size of a bicycle is based on the length of the tube component that holds up the seat. Most measurements are made from the top of the tube for the seat, into which the seat post is inserted to the centre of the front axle which is used in the assembly of the gears. As the size of the seat changes so does the entire frame in proportion to the frame size. Sizes of bicycles are quoted in different ways by different manufacturers—some use inches, some uses centimetres and others just use frame size, such as small, medium, and large.
The type of bicycle is also a determining factor in the frame size. For example, a road bike that has a frame size of 58 centimetres has a different size from a trail bike of the same frame size. Therefore, it’s important to know what kind of bike is being purchased before looking at sizing charts.
The frame size that people choose is also dependent on the type of biking that will be done, and personable preferences. Someone who rides a mountain bike and wants to ride more aggressively but may also want the bike to be more maneuverable may look at a bike size smaller than they usually ride. There is no right or wrong when it comes to bike sizes but it is based on what is comfortable and most suitable for the type of riding needed.
There's also a fantastic large frame size guide on this website.