If your mower starts with the turn of a key or the push of a button (instead of the yank of a recoil starter rope), it has a battery and a starter motor, just like a car. And like your car battery, riding mower batteries are almost exclusively 12-volt designs.
A typical battery on a riding mower is a lead-acid style, like a car battery. Lead-acid batteries are reliable and proven technology, but they're also heavy and hazardous to handle. Some mowers now utilize lead acid-gel batteries, with the electrolyte infused with silica. Gel batteries are more stable physically, with no need to sit upright, and the same is true with glass-mat batteries that use a fiberglass mesh to help contain and manage the electrolyte.
Buying Guide for Riding Mower Batteries
Riding mower batteries may differ from automotive batteries in significant ways, but they are classified and rated using the same system. Riding mower batteries are rated by cold cranking amps (CCA), which is the amperage that the battery can deliver at zero degrees Fahrenheit when cranking continuously for 30 seconds. Of course, unless you're starting a snow blower, you're not likely to be doing yard work at zero degree temperatures, but CCA ratings still give you an idea of what to expect with your battery.
They're also classified by physical size, which is important since the battery has to sit in the mower's battery tray properly and connect to the battery cables and clamps. Like a car battery, a riding mower battery is a rectangular box shape; most are 8.3" long, 5.1" wide and 7.25" high. The Battery Council International classifies these as U1 size. Check out the various sizes here to find the one that's right for you.
Like automotive batteries, riding mower batteries are a "get what you pay for" proposition. Check your battery for warranty period, cold cranking amps, and expected service life; compare that against your budget; and decide accordingly.