A disk usage analyzer is a tool to conveniently find out how much hard disk space different directories and files are taking up. It combines the effectiveness of the Unix du (if you never used it, stop here and do a man du in your command line immediately. If you do not know what that "command line" thingie is, whip yourself in the back repeatedly), with the convenience of a visual clue of how large directories are compared to one another.
From the two DUAs I mention, I largely prefer Filelight, for some reasons:
1 - When I want to open a terminal in a location chosen from the DUA window, with Baobab it's two clicks away: "Open file manager here", then "Open terminal here" in the file manager. With Filelight, it's just one click: "open terminal here". Plus Filelight has a handy locator bar at the top, showing the full path to the current location (useful to copy-and-paste with the mouse to an already open terminal).
2 - Filelight shows directories up to individual files. Baobab just dirs.
3 - With Filelight, navigation up and down (and back and forward) in the dir tree is a breeze (web browser-style). With Baobab, it's a pain.
4 - The presentation is similar, but the one of Filelight is slightly nicer, with more info when the mouse is hovered over the graph.
Probably Baobab can be easily made to behave like Filelight. I just tried them both, and liked the latter better on first sight. I tried Baobab first, and I found some things lacking. When I tried Filelight, five minutes later, I just thought "These are the details Baobab was missing!"