What is the purpose of multiple ethernet ports on my modem? [closed]

The ethernet ports are for connecting multiple devices within your LOCAL network so they can communicate with each other. The modem, assumingly, from your ISP provides ROUTING functions to the ISP from your network but only on the specific port that's allowed to do that.

The other ethernet ports would allow you to plug in say a PC, laptop and printer and them be all on the same subnet and be able to "talk" to each other. Basically it becomes a "dumb" switch for you to have a local network without having an additional switch.

EIT

Straight from the NetVanta documentation:

The NetVanta 838T is a Carrier Ethernet Network Termination Unit (NTU) that terminates up to eight e.SHDSL copper pairs. Four 10/100 Ethernet ports are provided for customer use.

So to reiterate what I said, they are for creating a LOCAL network (LAN) as opposed to adding an additional switch.