The Target Management System, accessed via the quickmenu or the slash-command /tm, is a straightforward way for the raid-leader to assign targets to the Main Tanks during a raid. It aims for more high-end encounters like the core-hound packs in Molten Core. For normal raiding i'd say it's rather useless. Well... maybe not useless, but it would be really tedious to maintain this way of targeting in Stratholme for instance.
The principle of the Target Management System is easy: You - as raid-leader - decide which targets the Main Tanks attack and you are now able to assign them to the Main Tanks.
After committing the /tm command, you are presented with the above window. Now you select the mob, that should be assigned and click on the Main Tank, who should target it. The Main Tank will now get a popup-message to confirm his new target. Repeat this until every Main Tank has the target, you want and you are good to go.