Except the monarch has to give the Royal Assent before any Bill can be made an Act.
The monarch has no role in parliament, but does have a role in government. This was established after the shenanigans of Charles I who ended up being banned from the Commons - hence the need for Black Rod as the monarch was banned from entering the Commons.
The monarch is the Head of State and is Head of the Church of England. They are the one who, after an election, gives consent to the person visiting the right to form a government and the one who can prorogue parliament - last used legally in 1997 when Major wanted to avoid any debate on the 'Cash for Questions' scandal.