A router chooses the “route” between networks: from the internal office network to the internet and back. A business router often handles extra jobs too — handing out IP addresses (DHCP), VPN and basic firewall protection.
A properly configured router is the foundation of network stability and security: for example, with two internet providers it can switch to the second one automatically when the first goes down.
Example
An office has two internet providers — when one fails, the router automatically moves traffic to the other.