A router is necessary to split an internet connection between various devices in your home, as modems are rarely, if ever, made with enough ethernet ports or with wi-fi capability necessary to do this on their own. Without a router you'd likely only be able to hook one device up to your modem. They also add a modicum of security as many have built in firewalls, but you should always employ a software firewall as well and not rely solely on your router.
