Same card in this system from which I'm typing this response. I bought the 9800gt because it's passively cooled - no fan = quiet & this is a media pc, so that's a clincher for me.
The connector is for SLI, which is Nvidia's system for connecting two graphics cards together for double the graphics performance I.e. it's aimed at gamers.
In fact I think they've droppped it as an idea recently, so for the purposes of sticking a new card in your box, don't worry about it, unless you specifically want to turbocharge Halo ten or whatever the kids are playing with these days.