What does the Queen do in Parliament?

The Queen's role in Parliament is formal and largely ceremonial, but important all the same. An Act of Parliament only becomes law when the Queen approves it. This is what's called the Royal Assent. It's a mere formality, however. Although the Queen could theoretically refuse to give her assent to Acts of Parliament, in practice she never does so.
After each General Election, it's a long-standing convention for the leader of the political party with the most seats to seek to form a government. If they can command a majority in the House of Commons, then they will become Her Majesty's Government, with each member of that government becoming a Minister of the Crown. This is a throwback to the days when government ministers were chosen by the monarch. But nowadays, the Prime Minister chooses the members of her government and the Queen formally receives each minister in a ceremony called the "kissing of hands."