The telephone lines can't handle the higher speeds that are needed very well. The telephone system is not the only medium that can be used to send data from one computer to another. Data can be sent through cable TV wires, through electric wires, and wireless microwave technology. A third thing that is needed is some system of telling packets where to go, kind of like the way a traffic cop routes traffic. Remember that the Internet is a collection of computer networks.
Routers connect two or more smaller computer networks on the Internet.
They also look at the IP address that is attached to each packet and decide which route through the network to send the packet so that it can reach the destination computer. ILC Glossary of Internet Terms.