An offer that is subject to the sale of a buyer's home is called a contingency offer.
The wording of the contract should allow you to continue to seek other buyers, and if another buyer makes an offer, the first buyer has a limited amount of time to remove the contingency and perform, or cancel their contract.
In recent years, most of the contingencies were waiting on the bank to accept a short sale offer. Because we are now in a different market, contingency offers now most likely are contingent on the sale of the buyer's present home.
In a normal market, similar to the market we are experiencing now, a buyer often has to sell before they can arrange financing for another home. Oftentimes, there will be a string of contingent offers in a row. For instance, if you accept a contingent offer and your buyer accepts a contingent offer from another buyer who has accepted a contingent offer, then when the lowest price home in the string sells, all the homes in that string will finally sell - one right after another. Or, if there is no sale, or an expiration of the contingency offer, none of the homes ultimately closes.
A contingency offer may be structured different ways - expiration date or none, cash forfeit or none, renegotiable or not, etc. Every buyer has a different conception of what is best for them.
So long as the contingency exists, and your home is on the market for other buyers, nothing is lost. If your buyer wants you to take your home off the market, then their offer should include cash forfeiture if they do not ultimately close the purchase - often in real estate this is referred to as an "option" to purchase.
This is just a description of a contingency offer, and should not be taken as legal advice. If you seek legal advice, please consult with your attorney.