That's a quick-disconnect system, sold at the "big box" hardware stores (under the "Comet" brand name, if I'm not mistaken). The piece attached to the spigot is the female fitting. The piece attached to the hose is the male fitting.

There are three rubber rings visible in your picture. The uppermost ring attaches the female fitting to the spigot. Grasp it tight and loosen in the usual way. (Penetrating oil on the threads at the top may help.) The middle ring is the quick-disconnect feature. Grab it and pull it up to release. (You may have to wiggle the hose with that ring pulled up to get it to release from the internal O-ring.) The skinny one on the bottom attaches the male fitting to the hose. Grasp it and loosen the hose in the usual way.

The main weak point of this system is that the rubber rings deteriorate with age and lose their grip on the pieces to which they attach. Ultimately, they'll fall right off. If you can't get enough grip via the rubber bits, you have no choice but to use a tool (e.g. some sort of slip-joint pliers or a pipe wrench). This will likely destroy whatever remains of the rubber, but you have no real choice.

Once you get it apart, some WD40 or silicone grease on the internal O-ring can make it work better/last longer. It's very convenient when working properly -- and a royal PIA when not (as you've discovered).

Looking at one store's website, this system seems to be sold under both the "Orbit" and "Melnor" brands. Others, too, maybe. Good luck.

Thanks - very helpful. I'll give this a try.

thanks this has helped me as well :)

Well here's an update on my end. I've gotten the system apart via the quick connect in the middle, but still can't get the other two pieces (top and bottom). I'm doing a lot of lefty but not getting much loosy.

On the top part connected to the spigot, I'm able to turn the rubber ring, but it looks like there's a part underneath that's still connected to the spigot pretty tight. I'll try hammering it off.

On the bottom part, the hose is turning but doesn't seem to want to come off.

I'll keep trying! Thanks again.

You may need another pair of pliers.

Jim's right. The female fitting on the hose will, by design, spin on the hose with less friction than the threads holding the quick-disconnect fitting onto it. On top of that, the combination of corrosion between the two pieces and the spring effect of the hose washer means you may have to apply some force to get it apart.

Squirt some penetrating oil between the black ring and the hose end fitting, then let it sit for a while. Then take an adjustable wrench or hose pliers and use it to hold the hex flats on the hose end. Grab tight on the black rubber ring (maybe with a rag to improve your grip) and twist. If that doesn't work, you'll need a second pair of pliers on the rubber ring, which will probably tear it apart, but you may have no choice. Putting pliers on the smooth end of the quick disconnect fitting probably won't work -- they'll slip. If the rubber part comes off, the fitting is knurled underneath which will give you a better surface to grab with the pliers. See the photo below:

What, you thought I hadn't been through all of this before? ;)

Oh, yeah, on the top part attached to the spigot, what's under the upper rubber ring is solid metal. If the rubber is turning but the fitting's not, it's because the rubber has lost its grip on the fitting. Go ahead and grip down on it with your pliers. Worst case, you rip up the rubber part, which isn't doing you any good anyway.