From your ISP, if you have one account then you are given one IP address. If you have two accounts, you can have two modems and two IPs from that one wire running to your house. However these are public IPs -- real public IPs that are on the Internet.
If you simply want to connect multiple PCs to the same account, then they need to share the public IP. Since it's not OK to have multiple devices with the same IP (how would we know where they go? that's like having multiple 123 Main St buildings in your town), they must have separate IP addresses. Since you only have one public IP, that IP is given to the router and it shares it with all your devices by assigning the devices internal IP addresses (192.168.X.Y, 10.X.Y.Z, or 172.X.Y.Z [with 16 <= X <= 31]). The router takes one private address for itself, has the public IP as well, and all your devices can see this private side. When they want to leave that network it goes through the router which is the gateway and enters your modem and out into the free world.
For this reason, any modem which has multiple ethernet ports on it is a router and anything which is just a modem will always have at most one Ethernet port (it could, in principle, connect only via USB for example).