T-Buffer, or Tirolli Buffer, is actually an overarching term. The T-Buffer enables a whole slew of features including depth of field blur, motion blur, soft shadows, soft reflections, and full scene anti-aliasing (FSAA). All these new features enable a more realistic gaming environment.
Depth of field blur can best be explained through experience. Stick your thumb about eight inches from your face and focus on it. If you have normal eyes, everything else around your thumb should be slightly blurry. Now try focusing on something behind your thumb. Your thumb should become the blurry object.
Currently, graphics cards render all objects with the same crispness. Aside from our myopic friends, reality has a slight degree of blurriness when distances are taken into account. Movies and television shows use this blurring method to call attention to speakers or objects. So instead of having to scan the image for what you should be looking at there are visual cues to point you in the right direction.
Let's move on to motion blur. Objects in motion tend to appear blurry because our eyes cannot take in enough data to fill in all the movement. As a result, the missing information is blurred over. Computers on the other hand can provide in excess of 100 frames per second (FPS) for many games. If you watch a movie or TV show, most televisions display frames at around 30 FPS (a bastardized 60, if you take interlacing into account). So why do we get pounding headaches when our computers dip into these badlands of framedom? Video cameras record everything going on. They capture all the details, whether it is blurry or crisp. In that fraction of a second when a shutter is opened and closed to capture an image the motion is also captured. This built in motion blur is why we aren't annoyed by video in television and movies.