collapse of the old society

The wet bulb temperature, in a climate context, is a combination of temperature and humidity high enough that evaporative cooling no longer works.

In other words, above the wet bulb temperature, sweating makes you hotter, not cooler. Think sauna.

Which means if you're outside without shelter and it's above the wet bulb temperature, you overheat and die.

The meme is envisioning people crowding into cooling shelters as wet bulb temperatures become routine in big cities in the next decade or so.