When you put an offer in writing, the seller has three options.
1. He can accept your offer, together with all the terms you specify, in which case you have a binding contract as soon as the seller has signed.
He can reject your offer outright.
He can come back with a counter-offer that modifies any or all of the terms that you have specified.
If the seller makes a counter-offer, the ball is back in your court. Your original offer is no longer on the table, and it cannot become binding. The new counter-offer will contain one or more changes from your original offer.
The most likely change will be in the contract price, indicating that the seller won't take your offer price, but this isn't always the case. Sometimes the seller will accept your price, but reject some other terms that you put into the contract - perhaps the closing date, or the allowance for repairs, or the length of the financing contingency period, or your request for the seller to contribute to your closing costs.
Whatever changes have been made to your original offer, you now have the opportunity to take one of the three steps listed above. You can accept the counter-offer, in which case your signature on the contract makes it legally bining on both sides, or you can reject it, or you can counter with further changes.
This process can continue for some time, although it is unusual for more than two counters to be put on the table before agreement is reached or one side declines to negotiate further.
Although it is preferable for all negotiations to be in written form right from the start, it isn't unusual for he agents for each side to discuss verbally any differences of opinion and to look for a mutually agreeable solution on an informal basis. This can save quite a bit of time.
The key to a successful negotiation, one that ends with a contract that is acceptable to both sides, is to be as flexible as you can, and to step back a little to take a look at the deal from the other side of the fence. An aggressive, confrontational approach is much less likely to end successfully.