So you've gone through the selling process. You've gotten your house ready, prepared for the sale, and finally you've almost reached the end. You receive your first offer on your house, so what's the next step? The first step for some may be to discuss the sale with a realtor if you are going that route. A real estate agent will be able to give you professional advice on how to proceed. Their experience and knowledge will also aid you through the selling and even the negotiation process if you're ready to go down that road.
So now that you've received your offer there are three choices: you can either...
Sign the deal, sell your home, and take the money. If all of the terms are favorable and you see no reason to do other ways, accept your offer and move forward with the sale.
If for any reason you want to back out of the sale, you don't like the offer and aren't open to further negotiation, you may reject. You may give or reason or not. This will end the selling process between you and the potential buyer leaving you to either take your home off the market or look for a better deal.
"Signing back" your offer simply means you're sending it back not as a "Yes" or "No" but rather to change or renegotiate the terms. You can sign back if you want to negotiate for more money, reconsider the closing date, get a home inspection first, or for any other number of reasons. It simply means you're sending the offer back for reconsideration, a bit of tweaking, and/or renegotiation. You may also sign back if you dissatisfied with any of financing options, for example you want a better downpayment, all cash, or whatever else the case may be. You may also sign back if you simply want more time to discuss the deal with your realtor or any other decision makers.
Just remember that the negotiation process can be a tricky one and even become heated for some. You'll have to consider with any sign back "Is this detail worth me losing the sale" if the answer is yes go forward, but if not you may want to consider closing the sale sooner rather than later, especially if you need to sell your home in a hurry. Once everything is done you can finally sign off on the final terms and your home is sold at last. Congratulations on making it this far, I think you'll find it wasn't as difficult as you first had feared.