What is this speaker cable connection?

What is your amplifier?

Well, not sure how expensive those connectors are in real life, but they are just typical spades. Unscrew the amp terminals and stick them in. :)

My amplifier is parasound a23 and Arcam Neo Solo. 

Yes, as erik said, the connectors are standard spades. Because the speaker terminals on the Parasound 23 are quite close to the bottom of the case the length of the barrel of those connectors might not give you enough room to bend the cable away from the amp. It might be necessary to raise the amp, connect the cables from the top of the terminals rather than from the bottom or connect them from the bottom at an angle.

Both of those amps have binding posts that will accept bananas, pins, bare wire and spade lugs like you have. Just unscrew the plastic red or black knob and insert the lug into the area that is exposed when unscrewing the post. Then tighten it back up, as tight as you can get with your fingers or gently give it a nudge with a pair of pliers. You do not want them to move back & forth. Make sure the + & - wires are not touching each other.

I'm calling a spade a spade

Yes but the most badly designed worst engineered spades I have ever seen. I mean that picture, its like a car wreck. You don't want to look, but you do, and then you just can't stop. What a mess. We should have a contest, who can spot the most flaws in this most flawed design?

Yes but the most badly designed worst engineered spades I have ever seen. I mean that picture, its like a car wreck. You don't want to look, but you do, and then you just can't stop. What a mess. We should have a contest, who can spot the most flaws in this most flawed design?

I agree with you about the ludicrous spade.   It is way too long and straight and I doubt it would fit any of the gear I own.    My speaker posts are recessed and I would have to put my amp on a 6 inch riser to give it clearance.

Even if It did fit I wouldn't use them.  With the long torque arm  you run a big risk of shorting if a cable gets bumped.

More photos :)

https://photos.app.goo.gl/d9WuhoJ8eHC4Uog56 https://photos.app.goo.gl/cDLkKPieMgABXEW49

So, lots wrong here.

Speaker terminals have voltage, and accidentally shorting them can damage your amp. You don't want long, conductive terminals here. Next, they look very hard. You want your spades to be soft, that improves how well they grip and stay put.

In terms of affordability, get some crimp on spades made of copper and use appropriate heat shrink to insulate them below the spades. Something like this will work. Of course, check your wire guage to be sure you get the right size:

https://www.partsconnexion.com/AQUEST-75459.html

Hey to these is that the core is copper. Copper is a great conductor and very soft.

I would just add some heat shrink insulation to insulate the portion below the spade. Heck, even wrapping electrical tape should do the trick.
Bob

I meant to type:

Key to these is that the core is copper.

+1 gdnrbob, the really easy clear solution is with a simple wrap of electrical tape.  No reason to listen to those that get all high drama about it, the connectors will likely work just fine.  As mentioned above, if they are too long to connect from the bottom, connect from the top.  Also, can't beat the price.

you can remove them, and put banana plugs on yourself

Spades are much better, connectivity-wise, in my opinion.
Bob

Thanks for the extra photos! The more photos the more problems we can see! They inexplicably screw a barrel over the thing, for no other reason than to hold the little red or black plastic ring. Brilliant! The spade itself, instead of being flat on both sides so it can fit in a range of terminals flares out making it both harder to fit and even harder to bend without breaking. More brilliance! Don't try and bend, anyone stupid enough to do all this other stuff is for sure too dumb to use quality metal that can bend without breaking. Odds-on favorite: Made in China. 

Looks like there's still one more barrel that should screw off. Inside near the spade there has to be something in there to crimp or solder the wire to the spade lug. If you're lucky then you can unscrew and throw that away, slide some shrink wrap insulator over the connection, and have a much improved spade lug. Still crap, but nowhere near as crappy as it was with all that other crap attached.

If you're lucky. With the brainiacs who made this though it could go either way. Could be they solder the cable into that big long tube.

Whatever. For entertainment purposes only. Should be abundantly clear by now we are well past wasting any more time with this. The worst spade lug in the history of audio has long since been unceremoniously cut off and thrown in the dumpster where it belongs. One half inch is stripped and the bare wire ends are twisted around and fastened in the terminal post.

Right? RIGHT???!

I could not use with my Arcam solo neo. It never stays there. I tried with KEF LS 50 and It did not work well. The always come off. That's the reason I have asked. 

Clip ‘m ‘n strip ‘m!  Then put on some simple decent bananas. get ones with at least 2 screws. Buy Parts Express # 091-3600 or 091-3610. Both good. BFAs are better than regular bananas. Got to be careful not to exert a shear force though, they can break off. 

If those barrels unscrew and reveal set screws holding the wire down I'd remove those ends and put these on instead.  I've used these on several custome built cables that are budget friendly.  These have a friendly angle for amp side as well as speaker terminals.  The downward angle is convenient on several speakers I have, do not put a high shear force on connections, locking and stackable and they're completely protected against accidental twist contact that could cause a short.

https://www.parts-express.com/angled-locking-stacking-banana-plug-with-dual-set-screws-poly-shell-an...

The downside of those Parts-Express WBT/ Furutech knock-offs is they’re made of brass, not pure copper or a high copper alloy like tellerium or beryllium copper. So they don’t conduct as well as better bananas.