Pyandonea- the Maormer practice "snake magic", which they've used to tame the local sea serpents. King Orgnum even uses them as mounts and bodyguards.
Akavir- obviously, the Tsaesci are golden vampire snakemen and/or samurai Borg. Moving on.
Yokuda- the Redguard version of Lorkhan is Sep, The Snake.

Also...

Thras- I'm pretty much grasping at straws with that one. The Sload do revere Mannimarco, though (pretty strange for them to be so fond of an Altmer, though). The King of Worms. I don't know if we can equate "worms" with "snakes" and/or "serpents", but they do have a similar sort of appearance, ie no legs. Could be a poetic connection. Not to mention the fact that Mannimarco became a god the same way (or at least similarly) as Talos. So we can probably assume that Manny is an avatar of Lorkhan, which going by the Redguards, is a snake.

So, just going by the above, every non-Tamrielic civilisation seems to be connected to snakes, and quite possibly Lorkhan in some way. And three out of four of them don't care much for Tamriel. The rebels to Tamriel's king, if you will.

So, what does this all mean?

Basically, snakes are cool.

More in depth:

Sea serpents exist because fins are lame, and it seems weird to us mammals that fish have so little flexibility across their body. So we come up with the sea serpent (which exists as an idea even when it doesn't exist as an animal), the ultra fish, and we make it huge because we like big stuff. Pyandonea is just where this particular monster ended up.

The Tsaesci are immortal vampires. The snake eating its own tail (ouroboros) is an ancient symbol of infinity or eternity. Snakes, like vampires, have fangs.

Yokuda was dominated by deserts, which are often dominated by snakes. Iirc, the Yokudan version of a lot of things are snakes. The Yokudans believe that most things are cyclical, and so once again they call upon the ouroboros symbol.

As for grand, in-TES significance? The Yokudans are the only ones to describe the form of high-level entities like anu, so by default, they are right. The whole of existence is a great huge snake.