This is the time of terrible Tudors we are talking about! Like in the Tudor horrible history book, "You don't tangle with a Tudor!". The Tudors were autocrats. They were very effective power brokers and hence survived. Forget the court being democratic or like a senate/parliament.
So as to your question: what was the court?
The court was the extended household of the monarch. It went wherever he/she went. Before modern times the monarch was the fountain head of wealth, land, power and jobs. Serve the King/Queen well and you might be rewarded. Therefore the court was the place to be. A chance to advance.
It was comprised of nobility and staff.
The nobility had land and wealth. In return for this land and hence wealth they owed the King/Queen there loyalty and service. In order to get more fields of green and coin they had to effective serve the Crown through war, governance, administration or other.
However the court wasn't just the warren of blue bloods. Oh no. Tudors unlike previous monarchs also relied on the middle classes and commoners. If they were very good at there job, that is.
For example Thomas Wosley, the son of a merchant rose to huge power under Henry VIII. Similarly Thomas Cromwell also rose to high office despite being the son of a brewer and butcher. However both these examples fell to ruin. Wosley died before trial and Cromwell was executed. When you served tyrants like the Tudors your life was on the line. If you angered them or failed them, then you could just be desposed off as fast as 3,2,1.
A significate part of the court was the Privy Council which was the top executive body of the Tudor monarchy from Henry VIII onwards (they met in the King's Privy Lodgings hence the name). When the Crown was away from London one group stayed in London and another group went with the Crown. It was the group with the Crown that gave the orders to London. The Privy Council still exists today although in a much more waterdown sort of way.
So there you have it. The Court - the powerhouse of Tudor politics.
History Learning Site
Elizabeth by David Starkey