A regulation is basically a rule or directive made by an authority. Deregulation is the removal, or cancellation, of certain rules or directives. (The prefix "de-" here means "remove.")
Governments set lots of regulations to create order and uniformity in a particular industry, like banking or manufacturing. When bankers and manufacturers don't like these regulations, they ask the government for fewer controls and restrictions, or deregulation. If your parents are constantly meddling in your life and you would like them to give you a little more freedom, you might consider asking them for deregulation. Your vocabulary might just impress them enough to grant it.