It’s a home automation protocol, like X10. You buy devices that can talk ZigBee to a hub device (probably can use a computer on your local network for this). From the hub you can do all the usual automation tasks.
To extend that slightly: it's a low-throughput, low-power mesh network that doesn't need the smarts or power draw of Wifi. Because it needs an in-home hub anyway, it's unlikely to die without Internet access, and devices on the standard have at least some level of basic inter-operability.
So if I wanted to say put a bunch of sensors in my house to monitor temperature over time without necessarily tying that info to my thermostat or anything, is this ZigBee thing a promising thing to look into?
Yes, and there is even a great FLOSS hub software Home Assistant [0] (though to be fair, it requires some tinkering compared to the proprietary systems) and if you run it on a PI or small server, you might as well get a conbee II which is a USB stick that adds Zigbee support directly :)
The bigger hassle seems to be different zigbee hubs that have varying levels of compatibility, so while you can pair the devices you can't get the data you want.
I've just been down the research rabbit hole, and about to try using zigbee2mqtt to bypass this nonsense (this also then means the only internet connectivity will be through a device you control)
Also systems like Philips Hue use ZigBee protocol. We have Hue lights at home and I'm planning to plug a ConBee II to my router for the Home Assistant to see how well I can run the lights with another hub.
Philips Hue hub talks to diagnostics.meethue.com all the time, and it gets kind of annoying already in the pihole stats.
there's also a difference between IoT and "look ma I wired an ESP32 to a DHT22 and sent data to timstream on my NAS". The latter is entirely you. WiFI isn't the issue, it's running cloud based hardware that can't work without someone's servers.