An offer is an official statement that signifies your intention to buy the property and how much you are willing to pay for it. An offer is delivered through your real estate agent to the seller. Unless seller already has accepted another offer, seller has option to accept an offer, reject offers, or counter multiple offers. Counter offer conveys what the seller wants from the transaction on top of the previous offer. Surprisingly, not every seller will counter an initial offer and accept the initial offer if they like it. Others will counter offer many times until they are satisfied.
Offer paper contains the price of a property and can contain other transaction details such as time limit of escrow period (sellers prefer faster escrow), money you would like to receive after closing, and what buyer wants seller to fix/update. There is one more opportunity to request for seller to fix after an offer is settled, which is after a house inspection (explained here).
Do you must buy a house when your offer is accepted and escrow begins? No, you can back out in most cases. Unless a specific grace period is stated on the offer (or counter offers), a default grace period (17 days in California) takes effect that lets you back out from an escrow for any reason. After the grace period and before the end of the escrow, you could back out from escrow by losing your deposit money which is usually 1% of the offer. Consult with your real estate agent for exact rules of your state.
When buyer’s offer is accepted by seller, escrow begins.