As the boiler in a HX cools down the steam condenses back to water and this can create a vacuum in the boiler.
When you next switch on the HX you can get a false pressure reading in the boiler as well (milk texturing problems) if a vacuum was allowed to form....
So the vacuum breaker is a very simple valve which is held closed by the pressure in the boiler and when this drops, gravity pulls the valve down, opening the boiler to the atmosphere and allowing air to enter...... as the boiler heats up the air is slowly expelled and when enough steam pressure is produced - it closes.
But they dont always work! They sometimes become stuck closed...... so good practice is to open the steam valve at shutdown to expel the remaining steam and then let air flow in..... and close it again when a steam is coming out of the wand at heat up.