Bridging just basically means you can run two subwoofers (or in this case a dual voice coil) using one amp/signal wire.
Without bridging you would just be running one channel to one speaker, or in your case one voice coil, but if you've got two, you might as well use them.
You can also bridge an amp to your running two channels to one speaker to increase power going to the speaker (more power = louder).
http://www.wikihow.com/Bridge-Subwoofers
But in your case, if you've only got that subwoofer (speaker) that you posted, you will most definitely need an amp if you want any sound to come out of it.
Guessing you don't know any specs of it, so it will be hard to advise you on what amplifier to get, but I reckon if you
really wanted to use that speaker (I do not advise), a fairly low powered (cheap) 2ohm capable mono (single channel) ampifier, or 4 channel amplifier if you would like to amplify front or rear speakers.
I had an edge ED7800 4 channel amp powering my subwoofer and front speakers in my clio, was around £80 but did the job.