What is an offer of a contract?
When you ask someone to do something, or offer to see someone for a price, you are making an offer. An offer is the first step in forming a contract. The middle step is the other party's acceptance of the deal. The last step is performance - where you each live up to your side of the bargain.
Words, gestures, or actions can signal an offer to enter into a contract and an acceptance. If you are forced to make an offer ("your money or life") it is not a valid offer. Similarly if you are tricked into accepting, it will not be deemed acceptance of the terms offered. To have a binding obligation on both sides, both sides must approve and accept the terms and conditions of the offer. Offers remain open until: (1) accepted, (2) rejected, (3) retracted prior to acceptance, (4) countered, or (5) expired by their own terms.
If you reject an offer, you have no contract unless at a later date a new offer is put on the table (called a counter-offer). A counter-offer is a new set of terms and conditions given in response to the original offer. The difference between the original offer and the counter-offer may be just one clause in particular or multiple provisions or the entire contract.
Be mindful that you can take back or withdraw an offer at any time before the other side has agreed to the deal. This is called retraction (proving that you have withdrawn the offer before the other side accepted may present a problem). On the other hand, changing your mind after you have signed or agreed precludes retraction. Absent compelling reasons for not holding up to your end of the bargain, you will be a party to a contract.