What else can you do with a wire nut ?

There are many names for these connectors:

wire nuts, wire connectors, cone connectors, or thimble connectors, but I always call them Marrette connectors. I may have a few around, but I don't stock them, so I never developed any new uses for them. Maybe you could glue some small ones on your shoelaces. (I have tried heatshrink on my shoelaces)

I wonder if they could be used as a pencil lead sharpener : )

Wire nuts are as rare as 4-leafed clovers in the UK. I've only seen them once, when Amazon supplied a couple within a box of parts to connect a Ring doorbell. I binned them, because I had zero experience with them. They look pretty strange to people who have never seen them before, as if they cannot possibly function : ) They are a successful product in North America etc.,  so I know they must function, but they still look odd, takes some getting used-to.

They work way better than any description would suggest. I was highly skeptical when I started my summer job as an electrician's helper, but they are really quick and seem to work well for at least 20 years.

Had to Google that .  I've used wire nuts forever with romex in my house wiring (3 houses so far) - so it's almost second nature to me.  I didn't realize they weren't used in the UK.  I have to admit that I've been horrified by some DIY wiring and seen the effects of not using them properly.  My son bought a fixer upper last year and we ended up replacing all of the outlets and switches.  I was surprised at how bad the previous wire nut connections were.

shabaz said:

Wire nuts are as rare as 4-leafed clovers in the UK.

Apparently for good reason, they used to be ceramic and were dangerous with 240v, so were ultimately banned. I'm not sure about newer types of wire nuts.

So what is used to connect AC wiring if wire nut is not used?

Pretty much almost always screw terminals, like these ones which are part of a ceiling light fitting. They come in plastic encased blocks too.

Plastic blocks that can be cut to the desired length:

The plastic blocks above are nowadays less popular, most electricians here now prefer Wago connectors like the one shown below, which is Wago 221. They are pretty awesome, handy to keep some for quickly assembling cables without soldering or screwing, its just a plastic lever that locks or unlocks the wire. They are reusable too.

What happens in a wire nut? Do you simply twist the cables together and put the wire inside the wire nut hoping it doesn't separate?

The wire nut has a spring inside that you screw onto the twisted wire. It does a good job of accommodating different twist geometries and the spring is made of strong enough wire that you can twist it on tightly. It acts like a multi-layer noose that gets tighter as you twist, ending up with continuous force squeezing the twisted wires with even more conductive wire, and it won't spontaneously loosen off. The plastic thimble provides grip to twist and insulation for the joint.

Ah yes I remember where I've seen these used now.

Telecommunications, they're typically used in phone line junction boxes in the UK, likely because they're low voltage.