This is a large topic. Lawn mowers, roughly speaking, can be broken down into two cutting types -
- Rotary mowers - have a metal blade, revolves horizontally (usually clockwise) under a cutting deck, to produce a regular cut. (see Fig 1.)
Fig 1. 
- Cylinder mowers - have a cylinder of blades that revolve forward, on a vertical plane against a fixed blade, scissorlike, to produce a very defined, sharp and low cut. (see fig 2.)
Fig 2.
Within these two cutting styles there are four main categories.
Wheeled Rotary Mowers - these four-wheeled mowers are popular, versatile and the most commonly purchased mower. Great all-rounders, they come in a huge variety of sizes styles, drives, cutting facilities and features. They work in all sorts of garden and terrain. Their coverage ranges from small to large gardens.
Roller Rotary Mowers - like the wheeled rotary, above, they are popular and have all the same benefits plus the added advantage of a rear roller to achieve the striped effect that gardeners, particularly in the UK, are so fond of. They give a good, even cut and all garden sizes are pretty much catered for.
Hover Mowers - these have a rotary action, but hover on a cushion of air so there are no wheels required for mowing. However, transport wheels are occasionally provided. These mowers generally have a lower footprint than other mowers and are relatively lightweight so are easy to store. They are ideal for small to medium sized gardens
Cylinder Mowers - these are nearly always fitted with a stripe-creating roller. Invented first and very traditional they come in a wide variety of shapes and sizes and the very top models are used for large, prestigious gardens and sports facilities.
Of course within all these categories there are many sub-divisions and choices of power, style, size and cutting width.