To build on what Devac said, e.g. the "spooky action at a distance" (spukhafte Fernwirkung) of entanglement is actually a successful prediction and self-consistency of our existing quantum mechanical model of the universe. It's a very successful model.

two-slit experiment

We do know how (or why? unclear in this context) the magic happens. The photon's wave function collapse occurs if a measurement of the photon is made as it passes through one of the two slits; then it passes through one of the two slits localized in space, as a particle, and is thus unable to interfere/interact at the slits like a wave. If the photon isn't measured at the slits, there is instead a pattern of many peaks and troughs observed after the slits, because the photon is behaving as a wave, as indicated by the wave refraction physics and resulting interference pattern produced by the slits. The wave interference pattern is only significant/noticeable because the separation between the two slits is close to the photon's wavelength. At large, people-size scales, the same, small wavelength (say, visible) photon behaves more simply, and we are able to treat the physics more simply than with quantum mechanics, like with e.g. geometric optics.

And that's really the crux of all physics models, actually; It's always about scale-size. And sometimes a characteristic scale-time. Where I physics, it's the average radius of gyration and the average time an electron takes to gyrate around the local magnetic field (~1 km and ~1 ms, in my very specialized neck of the woods, about 11 Earth radii sunwards of Earth), but it's much smaller and quicker for quantum mechanical dynamics, typically, like modeling the way an electron recombines with an ion in a plasma to form a neutral atom, which usually occurs on scales of nanometers and nanoseconds (or faster!), approximately.

Bottom line is we know wave function collapse happens, and how to cause it, and how it's happening all the time, every moment, even just because your personal matter is interacting with the environment around you, on top of with itself. But who knows how to interpret it. Have you seen Everything Everywhere All at Once? I haven't. But the existence of the multiverse is one fairly common interpretation of wave function collapse. There are some other juicy and recent propositions Devac linked in response to my original comment, too.

Whether or not another, better model of the universe might unlock a very clever method of transmitting information via entanglement... is a question that I just thought of, but for now, we believe that it is impossible to transmit information using entanglement. Information transfer would require interacting with a subset of the entangled system, which of course causes wave function collapse of the entire entangled system, which then prevents instantaneously sending information between the spatially-separated subsets.

edit2: Hahah, gaming this out even more simply, I call my buddy, to whom I gave one of my two entangled matter boxes, and I'm like "ok so #1 is up!", and then wait to hear back "#1 is down, over here..". Ultimately, I am not able to exchange information more quickly (past lightspeed) than I would have been if the matter we're describing wasn't entangled. I didn't know mine would be up, nor did my buddy know he'd measure down, and I can't encode a message if I don't know (in the simplest case) if I've got the zero particle or the one particle. So, we think faster-than-light information exchange simply doesn't take place. But black holes get weird. And maybe other sectors of the universe, dunno.

So we can currently point at something that makes no sense and say "that's quantum entanglement", but we cannot say how it works or why

It makes some sense, at least. Not the most. How entanglement works or why? I have trouble like ascribing meaning to a coat hanger a panhandler bent into the shape of guitar that I display on the desk I play my guitar next to, so I guess I'm mostly sitting this one out.

I am gonna get back to Devac's other reply, but first I wanna go through my own (bullshit) cosmological model of the universe for a couple more days. And some other ideas.

is it something we can use in some way?

Oh do we ever already. There are so many applications of entanglement, including quantum computing. Some applications are intentional (lol bose-einstein condensates could never arise "in the wild" on the surface of Earth except for in our top laboratories), and some may arise as a side effect of requiring something like guaranteeing a secure method of quantum cryptography; If 1/2 of the entangled system's wave function was already collapsed before you measured it, someone accessed the information, causing the whole entangled system to collapse.

It almost sounds like gibberish, sorry, I know, but these are an attempt at concise, yet sweeping statements built on having suffered through some maths. Navigating the delineation between where the model ends and interpretation begins is a very healthy exercise, especially for experimentalists like me.

edit: Some of my QFT, standard model, and information theory isn't quite right, I think, and I'm looking forward to any corrections, no worries :).