The "contract" is the final bid that the game will be played in.
The contract can either be a "suit" contract or a "no trumps" contract.
In a suit contract one suit is designated as the "trump" suit. A no trumps contract is what it says - there is no trump suit. When the game is being played (see lesson 5) a trump card wins the round if no other trump card is played.
Once the contract has been decided the person who first bid the suit (or no trumps) that the game will be played in becomes the declarer. Declarer's partner becomes the dummy. The person on the declarer's left plays the opening lead.
What does the contract mean?
Once the contract has been decided the declarer and their partner are aiming to make the number of tricks that they bid for. The first 6 tricks don't form part of the bidding.
There are 13 tricks in each round of bridge. A bid of, for example, 1 spade means that the partnership think they will win 7 tricks - the six non counted tricks plus the one trick that they bid for. A bid of 7 hearts means that the partnership think they can win all 13 tricks - the six non bid tricks plus the 7 they bid for. A bid of 3 NT (no trumps) means the partnership think they can win 9 tricks (6 + 3).