Wolfgang and Crash have given you some good information here.
What makes a weed fin different from the speed fins and vertical
race fins that Wolfgang mentions is the leading edge angle.
Take a look at the Lessacher Design website and his Duo weed fins
As you can see the leading edge angle is swept back at 45 degrees or more.
What this does for you as the sailor is it allows any weeds that would catch and
collect on the leading edge of a more vertical (< 45 deg.) to be flushed off the leading
edge but the water flow.
Wolfgang's assymetical foils give the additional weed shedding feature that any weed that lands and sticks on the leading edge won't stay as the foil allows one end of the weed strand to "flap" slightly on the more concave side of the foil and be flushed off.
Additional benefits of a 45 deg. or greater leading edge angle occur if you run into some floating or submerged objects (turtles, fish, logs, trash bags). or if you run into a shallow area .
The angle of the fin will slow your board more slowly and actually tends to "lift" the back of the board.
This is a real safety feature if you sail in shallow areas with changing tides and sandbars.
A slow trip over the front of the board, on a weed fin, vs an hard slam over the front on a vertical fin
will almost always be much easier on the sailor, the rig, and the board.
Hope this helps,