If you begin, start, or commence something, you do it from a particular time.

There is little difference in meaning between these words, but commence is used in formal English. It is not used in conversation.

1. I had been asked to chat to the kids before they began lessons for the day.
2. As they saw him coming they began to dance.
3. The meeting, then, is ready to begin.
4. He tore the list from the pad and started a fresh list.
5. Mrs Bixby put a hand up to her mouth and started backing away.
6. The war started between England and France.
7. Students may commence a two-year Training Study in a chosen activity.
8. The space probe commenced taking a series of photographs.

Start has some special meanings which are not shared by begin or commence. You can use start to say that someone makes an engine or machine begin to work. You can also use start to say that someone creates a business or other organization. In stories, start is used to say that someone begins to move in a particular direction.

9. He couldn’t get his engine started.
10. He scraped up enough money to start his restaurant.

Note that commence cannot be use with a ‘to’-infinitive. You can begin to do something, or start to do it, but you cannot commence to do it.