Anti-sway bars go by many names. Sometimes they are referred to as anti-roll bars, roll bars, or sway bars...but they all do the same exact thing: tie the left and right suspension together so that the car corners flatter.
 
The sway bar is basically a spring that mounts to the left and right suspension somewhere, then is secured to a solid part of the chassis. It works like a torsion bar, by twisting. Naturally, a larger bar is going to be harder to twist so it is desirable to upgrade the sway bar from stock size to improve handling.  
 
The rule of thumb for suspension is that firming up the front will give more stability going straight, and help the car track more carefully. It also can help cure problems with oversteer (where the rear of the car swings out in a corner). However, upgrading the front bar can have the negative impact of inducing understeer, which is going to make the front tires slide  into turns and be generally bad for cornering.
 
Get a front sway bar when you are interested in high speed maneuvers on large sweeping corners. This is not a very common upgrade on TSXs. Most people opt to upgrade the rear only.
 
The rear sway bar is the most commonly upgraded suspension part in a front-wheel drive car, after shocks and springs. The rear sway bar helps make up for FF cars' tendency to push, or understeer, into corners. Upgrading the rear sway bar noticeably improves handling on the TSX without compromising ride quality. This part is easily the most Bang for the Buck you are going to get out of your TSX suspension.  
 
Sway bar endlinks provide the movable connection between the sway bar and the suspension itself. On the rear of a TSX, this connection is to a metal bracket bolted to the suspension knuckle. Sway bar endlinks can become a weak link in the suspension because they are under a lot of force when the car is driven harder than normal. This is especially true of cars with suspension that has a lot of travel.