Contemporary context
The elaborate rituals of the State Opening of Parliament would initially appear to have come straight from the formal ceremonial days of the Middle Ages. In fact the ceremony as now performed was devised only as recently as 1852, and many of its elements have their origins from events of the 17th and 18th centuries.
The monarch's Great Council
So it is not so much the ceremonial aspects of the State Opening which can take us back to the Middle Ages, but rather the people involved and what they symbolise that is the clearest reminder of the origins of Parliament. Parliament began as the monarch's Great Council and the central role of the Queen at the State Opening reminds us that it is still formally 'her' Parliament.
Furthermore, the hierarchies among the trinity of the medieval Parliament are made clear. The monarch sits on the throne located in the House of Lords and addresses the peers first of all, in effect recreating the Great Council of monarch and noble advisers which formed the first core of Parliament.
Subordinate Commons
The House of Commons, the junior partner in the trinity, is then allowed into the Lords' Chamber only at the monarch's summons, and even when it arrives, its leaders have to stay outside the bar - a wooden railing across the entrance to the Lords' Chamber, making clear their subordinate status. Nevertheless, the Commons asserts its independence during the ceremony by ritually slamming the door of its chamber in the face of Black Rod, the Queen's representative, who goes to call them to attend on the monarch in the Lords.
The Queen's Speech
The monarch then informs the members of both Houses the agenda of business for the session. The monarch's speech has for a long time been written by the Government then in power and reflects its programme, but every year there is still the ritual of the Queen's (or King's) Speech where she informs 'her' Parliament why she has summoned them.