I got into an argument somewhere, and need sources and explanations about what the Towers that, from what I understand, hold Mundus together are - pretty much all information available.

http://www.imperial-library.info/content/nu-mantia-intercept has some information on this.

...can I get a less-opaque explanation?

The less-opaque version is up to interpretation. Earlier today I saw someone claiming that someone else had gotten their Tower lore mixed up: "They don't keep Daedra out, they just keep Mundus from dissolving back into Oblivion." I have yet to see the rebuttal, so who knows what's right or wrong without reading the Intercepts? Still, if that paraphrase is correct, then the purpose of the Towers is indeed to prevent the Mundus from breaking apart. At the same time, though, the Towers have been going "offline" for the last several games, starting with Daggerfall, as either they or their Stones are removed from play. At this point, very few of them are left, which is one reason to believe that they are no longer necessary at all (after all, they're offline, but Mundus is still here). Most people theorize that Talos has taken over the purpose of the Towers himself (being a replica of Lorkhan, he therefore is intrinsically linked to Creation), which explains why the Towers' failure hasn't led to the dissolution of Mundus. That is, however, just a theory.

Note that I've given no sources of my own to back this stuff up, so I could be just as wrong as the next guy. I haven't read the Intercepts in a few months, nor am I very well-versed in Kirkbridese.

The Towers are all unique, and do different things. Its difficult to make a sweeping statement about them. The best I can do is that most (all?) are emulations of Ur-Tower, or Adamantium, on Balfiera Island, where the legendary Convention of the gods is supposed to have taken place. All towers are also places of tremendous magical power and function as the fulcrum of the dominant cultures that surround them. The Nords were breathed into the world atop Snow-Throat. The Chimer became Dunmer and the Tribunal became gods at Red-Tower. And the significance of White-Gold and Crystal-Like-Law to their respective cultures is equally well known.

THE tower is the secret to the universe. Or at least a secret. Its the sight you see when you look at the universe sideways. Anu and Padomay touch (like two bubbles) and where they touch it makes a Tower (like a line or an "I"). This is the image Lorkhan saw that told him the secret of CHIM, that all of reality is a dream, that he is part of that dream, and yet he still exists as an individual.

The first tower on Mundus was the Adamantine Tower. This is the "gift limb" or spaceship of Auriel who drove it into the Mundus to stabilize creation. When Adamantine tower landed, time began to flow linearly, ending the dawn and allowing the et'ada (original spirits) to take solid form.

The other towers are echoes of this first Tower. Red Mountain, where Lorkhan's heart fell. Snow Throat, where Kyne breathed life into the Nords. Crystal-Like-Law, which the Altmer use to try to re-reach the divine. White Gold Tower, built by the Ayleids for the same purpose (using a different method.) Falinesti, the walking tree city of the Bosmer. And the Orichalic Tower, lost in the destruction of Yokuda. Others speculate about additional towers.

They have some important metaphysical function. White-Gold Tower is a source of conflict, its what everyone fights over. Its why the Akaviri continually invade.

They solidify creation and/or prevent Daedra from entering the Mundus. They are sources of power. In the Elder Scrolls Novels by Greg Keyes, Umbra is seeking White-Gold Tower because he needs its power in order to be able to fully materialize on Nirn. Otherwise he is stuck in his stolen pocket of Clavicus Vile's realm.