What is this wiring panel and what are these Ethernet "ports?"
It's just a 110 wiring block. More or less a type of punch down block.
(According to a quick Googling, that wiring block is generally Cat5e compliant these days, so you could use it for a 100Mbit network connection). Instead of a patch panel Which has a set number of jacks pre-sized and pre-wired to a certain standard (like RJ45 jacks or RJ 12 jacks or whatever other standard), it's manufactured with exposed wire pairs so that it can be used for different standards easily (and is why teclos use them over patch panels that are fabricated for a specific standard only).
They could use that block for any number of different types of data connections, instead of being restricted to one. The drawback, which you note, is that they won't take a standard RJ45 connector, and require those odd plugs instead. Being for a 110 wiring block, they take 110 plugs. Though, actually, like a punch down panel, you could strip one end of your cable, and attach the individual wires to the individual slots on the wiring block as well, and it would work.
Here's an install guide for a 100 wiring block I found (with pictures) that might help give you a better sense of what that thing is - a standard plastic block with a bunch of wires connected to it... a description which would also apply just as accurately to the RJ-45 patch panels you're more familiar with.
Those are 110 punch down blocks with 110 to RJ45 cables.
That's called an AT&T MD110 punch-down patch panel from the late-80's/early-90's - I used them, they were 10Mbps only.