When it comes to modifications, you can put anything you want on the Jeep - lift kits, winches, bumpers, whatever - but you really can't go everywhere without a proper set of tires. Stock Wrangler JK tires and all-terrain tire replacements are fine for the on-road daily driver crowd as these tires utilize a tread pattern and sidewalls that are not geared toward off-roading. However, if you are modifying your Jeep and want to expand your off-roading presence, then a more aggressive mud terrain tire will help overcome just about any trail.
All terrain tires are the most common type of tires around. They perform well at high speeds, while also giving adequate performance in light off-road conditions. These tires are typically quiet, perform well around town, and employ a tread pattern that can shed water so the tire can stay in contact with the road. Most people can usually expect around 40-60K miles before all terrain tires need replacement. Mud terrain tires, on the other hand, utilize a wider type of tread that allow it to work best on uneven, muddy, or rocky surfaces. These treads almost act like hands to pull the vehicle up and over obstacles, while the tire's stronger sidewall protects against puncture when the tire is up against rocks or other sharp objects. While you can certainly use mud terrain tires on pavement, they are louder than all terrain and the will wear out faster while providing less fuel efficiency.
Once you decide which type of tire fits your plans, choosing the correct size is next as not all tire sizes fit every rim - especially when you are upgrading tire size. If you are just replacing your current JK Wrangler's worn or inadequate tires, the easiest way to verify what you have is to check the tire sidewall. For example, on a 2015 Jeep Wrangler Sport, the tire may read P225/75R16. In tire jargon, that just basically means the 'P' stands for passenger tire; this could also read LT (for light truck) on some tires. The 225 is that tire's width in millimeters and the 75 is the tire aspect ratio - relationship between the sidewall height to width. The R (for radial) should always be standard on just about every tire, however some may read 'B' for bias meaning the tire's body cords run diagonally across the tire instead of radically. These kind of tires are designed for off-road only use and can be dangerous if used on pavement because of their construction. Finally, the 16 indicates the tire's diameter so this particular example means it fits a 16" wheel. For more information on reading these measurements, you can check here. Also, some tire manufacturers list their tires in inch measurements instead of metric, so here is a handy conversion chart.
For those looking to improve their JK Wrangler's off-road capability, or give it a more rugged look, then larger more aggressive tires are certainly on your list. However, in doing so, you probably will need a suspension or body lift to accommodate the larger tires. You may also need to change rims as well because a larger tire in the size you want may not be offered in your JK Wrangler's current wheel size. You also may need other modifications as well and you can check here for further information.