This is one of those terms that sound waaaay more complicated than it really is. It is of, of course, the date on which an offer expires. Until that date, the seller can accept (i.e. sign) the offer and create a binding contract. After that date, the seller can still sign and return it, but the buyer has the right to approve one more time before there is a contract. In other, more-legalese words, if the seller signs the offer after the expiration date, it is a counteroffer subject to the buyer’s approval.
In addition, any counteroffer by the seller terminates the offer. So in most instances the Offer Expiration Date is irrelevant, because in most instances a seller will counter on price if nothing else.