Sway bars -- AKA anti-roll, roll and stabilizer bars -- are one of many different suspension components used to fine-tune a car's handling and ride characteristics. Your vehicle doesn't necessarily need them to make it down the road, but they're rarely a detriment as long as the road is where your car stays.
Sway bars are long, spring-steel bars that connect the left and right-side wheels together and bolt to the chassis in the middle. If both wheels go up or down at the same time, the bar does little to nothing. However, if one wheel goes up while the other goes down (as in the case of body roll on a curve), the spring bar will twist and add some resistance to the car's net spring rate.
Anti-roll bars are supplemental devices; their primary purpose is to fine-tune the car's handling balance, not to increase its net handling limits by increasing spring rate. Installing a very thick, very stiff sway bar effectively ties the two sides of the suspension together, causing an independent suspension to act more like a solid axle.
Off-roaders will often remove or disconnect a sway bar's end links when hitting the trail. The sway bar's ability to tie the wheels together will ultimately limit suspension articulation, which hinders the truck's ability to traverse large obstacles and gullies.
