Queen and Government

As Head of State The Queen has to remain strictly neutral with respect to political matters, unable to vote or stand for election. 

But The Queen does have important ceremonial and formal roles in relation to the Government of the UK.
The formal phrase 'Queen in Parliament' is used to describe the British legislature, which consists of the Sovereign, the House of Lords and the House of Commons. The Queen's duties include opening each new session of Parliament, dissolving Parliament before a general election, and approving Orders and Proclamations through the Privy Council.

The Queen also has a special relationship with the Prime Minister, retaining the right to appoint and also meeting with him or her on a regular basis.

In addition to playing a specific role in the UK Parliament based in London, The Queen has formal roles with relation to the devolved assemblies of Scotland, Wales and Northern Ireland.