The Monarch can veto legislation in theory, but absolutely cannot do so in practice. He or she has the technical right to refuse “Royal Assent”, without which an act of Parliament cannot become law. However, Parliament is sovereign, and could pass another act overruling this veto, and probably abolishing the Monarchy in the process. So no matter how much Brenda despises any law, she has to hold her nose and sign it.
The Monarch is the head of state. Not all countries combine the functions of head of state and head of government - the USA does, but even other republics (like Ireland) do not. The Monarch represents the UK as a kind of embodiment of the state. This is ceremonial. Of course. The UK armed forces technically answer to her, not to Parliament. She is the Big Army Boss, or whatever her rank is.
The Monarch appoints people to the House of Lords*. She does so on the advice of the Prime Minister. There is no law that I know of that says she can’t add her own people to the list but if she made a habit of it, there soon would be.
The Monarch calls elections to the House of Commons. She does so on the request of the Prime Minister - see a pattern here? She “dissolves Parliament” by Royal proclamation, at which time all members must seek re-election on a date declared by her but, of course, determined by the Prime Minister.
When those elections are complete, she invites the leader of the winning party to form a government, henceforth to be known as “Her Majesty’s Government”.
Her Prime Minister must discuss national affairs with her regularly - once a week in normal circumstances. When the Parliamentary session begins each year in the autumn, she makes a speech (written by the Prime Minister’s staff) detailing what her government will do in this session. This speech is made in the chamber of the Lords; she is not allowed to enter the Commons, at all, ever.
All this said, her political informal political influence is hard to quantify.
*House of Lords is a weird one. You are correct in assuming that it is not trivial - since it does indeed have the power to delay legislation. The Government Act of, um, 1928? allows the Commons to ultimately overrule the Lords but still, it’s not a power invoked lightly. When it is invoked, the bill is presented back to the Lords, who don’t get to vote. They are simply told that the bill is passed “because the Queen wishes it”.
Edit for accidentally omitted negatation.