Parliament's role in the government of Britain changed a great deal during Eilzabeth's reign, and the role of the House of Commons became more important. However, the House of Lords was still more important at the time, and although Parliament was a useful tool for her she used it rarely. In her 45 years on the Throne the Houses sat for less than three years.
The Queen was still expected to live off her own money, with Parliament used to raise funds for extraordinary circumstances such as war. No royal head of state in Europe was really able to do so, and hadn't been since the 14th century at the latest, so Elizabeth frequently was forced to sell lands or become involved in various business enterprises. These included privateering expeditions, largely against the Spanish interests in the New World. She only called Parliament when she wanted to raise taxes. The House of Commons threatened to cut off her funds if she didn't marry, but didn't dare to actually do so.
She did use the House of Lords to push through the Act of Supremacy, which made her head of the Church of England. This allowed tolerance for radical Protestants and acceptance of Communion for both Catholics and Protestants. She also got the Act of Uniformity passed, which imposed the Book of Prayer on Churches in England, thus forcing through her own religious policy of turning Great Britain into an overwhelmingly Protestant nation.
Elizabeth disliked long Parliaments, which forced the Houses to streamline procedures. It was during her reign that the Houses adopted reading a bill three times. The House of Commons did become a far more useful political tool, largely through balancing their policies and procedures with the House of Lords. Of 506 bills passed by Parliament during her reign, she vetoed 70. Many of these were considered "private" bills, not public, meaning they pertained to purely local activities such as village fairs and local markets. Her only use of Parliament as an advisory tool was during the debate on the execution of Mary, Queen of Scots.
Parliament improved dramatically during the reign of Elizabeth I, and the House of Commons gained much political ground, but the House of Lords still carried more weight. Parliament as a whole was a tool Elizabeth used only sparingly, and in ways she could mainly control.