A modem, sometimes referred to as a router, allows you to connect to the internet.
At Flip, pretty much any modem/router will work as long as it's ADSL2+ compliant. You can find that out in the manual, it's also usually on the box somewhere.
If you've had broadband before (or have it connected at your place at the moment) use that modem - no need for a new one.
The only exceptions are Orcon Genius and Motorola modems.