If you have cable for internet service you need a modem that converts coax to ethernet.
If you have DLS for internet you need a modem that converts phone to ethernet.
As stated there are "grey" devices that are a modem and router together. Cable usually leases you a modem and you provide your own router, while DSL will usually lease you a modem/router combo.
Thus what you need completley depends on what your ISP is and what technology they use (DSL, Cable, Fiber, etc), and what equipment you already have.