What is the purpose of an vacuum breaker on either my hose bib or my laundry sink ?

The vacuum breaker allows air to flow back into the system piping instead of whatever is in your garden hose or laundry tap hose, in the event of a reverse draw on the city water supply. eg. If a firetruck hooks up to a fire hydrant on your block , it will pull all of the water out of the lines in your house. If you had a sink full of dirty water in your laundry sink with a hose from the tap into the water, it would pull the dirty water back into your house water lines. The same thing would happen if you were spraying your lawn with weed eater, it would be pulled back into the city water supply, poisoning the water.