What is a modem compared to a router
A modem is what you use to actually receive your internet connection through phone line or cable. A router splits that connection up so you can use it on multiple computers
A modern is a physical device that connects internet by the use of one network service provider. Router can carry internet signals from various network providers. Read more on http://whatismyipaddress.com/routers and http://compnetworking.about.com/od/modems/g/bldef_modem.htm.
Modem connects to the network, router connects to the modem and most commonly transmits wireless data you can use a modem without a router but not a router without a modem