A short sale is when the owner of the property owes more then what the property is worth.
The seller lists the property at current market value. When they accept an offer, they take the offer to the lender and ask the lender to approve the offer. If the bank chooses to accept the offer, the lender will take the amount the house sold for and forgive the difference that is owed.
For example: The seller has a $300,000 mortgage. They sell the house for $275,000. The bank gets the $275,000 and forgives the remaining $25,000 that is owed to them.
There is a little more to it then this but that's the jist. The seller needs ot be in a financial hardship position, can not have any other assets and can not receive any money or gains from the sale.
For a buyer, any offer accepted by the seller is subject to bank approval. However, all negotiations are done though the seller not with the bank. It can take months to get a response and buyers should be prepared for a long process. Usually the property is sold as-is, no credits for repairs and in some cases the buyer may be responsible for some costs needed in order to close