Brexit: This refers to the withdrawal of the United Kingdom from the European Union and Euroatom. Imagine if our eldest sibling England decided to move out and live independently away from its extended European family.
Commonwealth: A political association of 54 member states, nearly all former territories of the British Empire. It's like if after moving out, England still maintains close ties with its old roommates who used to live under British rule.
The British Empire: At its height in 1920s, it was among largest empires in history including parts in Africa, Asia, Americas and Pacific - making UK influential worldwide. Like being parents to many children around globe who have now grown up into independent nations.