What a broker is
A broker is the company that lets you buy and sell shares, funds and bonds on stock exchanges, and keeps them in an account in your name.
The middle person
You can't walk into a stock exchange and buy a share yourself. A broker (Interactive Brokers, Trading 212, Freedom24 and many others) is licensed to trade there for you: you put money in, press buy, and the broker does the rest.
Your shares are yours
What you buy is held in an account in your name, kept apart from the broker's own money. In most countries regulators check this, and many also insure accounts up to a limit if a broker fails.
What a broker charges
Brokers earn from fees per trade, currency exchange, interest on cash, or a monthly fee. Small differences add up over the years, so it's worth knowing what yours charges.