A Short Sale is home for sale as a result of two conditions: 1) the seller is unable to continue making the mortgage payments, and 2) the home will sell for less than the amount due on the mortgage(s) (so the sale proceeds will be "short" of paying the mortgage). When a home is listed for short sale, the lender has the right to approve the terms of the sale, since they will be losing the difference between the amount owed on the mortgage and the net proceeds of the sale.
That is only important to a buyer because lenders typically take several weeks, and several months is not unusual, to respond. Six months is my longest personal short sale experience, six weeks is my best. Their response is not always "What a generous offer. We accept". They may reject an offer outright or may make a counter offer. If they do make a counter, it is generally non-negotiable, and the buyer can take it or leave it. So it's possible to make an offer, sit in limbo for six months and then find out you're back to shopping for a home all over again.
A short sale differs from a bank owned sale (known as an REO – an acronym for the entry on the bank's financial statements – Real Estate Owned). An REO home is one on which the lender has completed the foreclosure process and now owns the home outright. Those proceed mostly like any other sale, and mostly in a timely fashion.
Many people think they can buy foreclosures at substantial discounts from what a market price would dictate. That is not true. Bank owned homes may sell for, or above "market" price. Depending on the market they may also sell for as much as a five per cent discount, but not generally more, if that.
Stories you hear of substantial discounts usually neglect to include that the condition of the home is substantially worse than similar sized homes on the market, so they are not really "comparable" homes. Cash buyers can usually buy at 5-10% below list price (bank-owned or private), because a seller values the fact that a buyer's loan approval (or complications with) will not cancel the sale.