They make the yoghurt, then pasteurise it (I guess so it has a longer shelf life). So it tastes roughly like yoghurt but doesn't have any of the good bacteria. I've also seen that sometimes lactobacteria are then artificially added back in so that they are present but in a controlled way.
It refers to whether the yogurt is alive or dead. It's not exactly mysterious terminology.
You get yogurt by using bacteria to process milk. In order to do their processing, the bacteria need to be alive. So, for example, adding living yogurt to milk will get you more yogurt, but adding dead yogurt to milk will get you milk with some dead yogurt in it.
I agree it's not mysterious. I was asking with some admittedly false naivety because if I'm being honest, I'm skeptical. I've only ever heard about this from people whose opinions on nutrition are dubious in other ways, and it's usually phrased as something like "all the yogurt you get from the store is dead." I eat yogurt every day and I sometimes make my own (using commercial yogurt as a starter), and I've never had a batch fail to start. Apparently I've only ever bought the live stuff.
A quick rule of thumb is that if the alleged yoghurt does not need to be stored refrigerated it is a "dead" yoghurt — i.e. not allowed to be marketed as a yoghurt in many markets.
Whether or not refrigerated yoghurt-ish products are live or not is another question. If you live in a jurisdiction which restricts the term "yoghurt" to products containing live cultures, you can rely on whether or not the refrigerated product uses the term in its description. Otherwise I have no idea.
Heat treating / pasteurizing the yogurt after making it, kills the bacteria in it. Now the yogurt is "dead". Actually it is the bacteria that are now dead.