My first satellite antennas were the M2 Eggbeaters with the radials. To answer the OP's question, AK5B accurately describes how the radials function and how they're hooked up to the transmission line.
In terms of how they work, they got me on the air on satellites. I was even able to upload and download emails from some of the early orbiting 1200 baud BBS satellites (like AO-16). I also fondly remember my days on the RS series of satellites (RS-10, RS-12 and RS-15). I used my Eggbeaters for 7 years. For the record, I did have mast-mounted preamps on them.
In 1999, I moved to a new QTH and put up CP yagis. There is truly no comparison between those (14 elements on 2 meters and 30 elements on 70cm, again with mast-mounted preamps) and the Eggbeaters. Also, I believe that today's satellites have lower power outputs than those old ones, so I don't know if the Eggbeaters would be as effective with the newer birds.
In short, if you've got no alternatives, the Eggbeaters will probably get you on the air and will certainly do it better than a ground plane antenna on 2 and on 70cm. But, if you can lay out the cash and have the room, I'd go with the M2 LEO pack at a minimum.