Why does a router need multiple internet addresses?
It doesn’t need multiple internet addresses, it assigns them. It takes the IP that is assigned from your ISP, and splits that up into separate IP addresses. If two computers were trying to use the same IP address to surf the internet, when a website sends information to the ip address of one computer, it would go to both of them, because the website sends the information to the IP address. What the router does is takes that information, and distributes it to the proper computer on the network. It uses (usually) 192.168.1.x where x is a number 1 through whatever, depending on how many computers have been connected to the router.