A presentation copy is one the author gave away personally, usually with an inscription recording the gift. Strictly, it is a copy given by the author, not one signed at a public event for a buyer, and the inscription normally shows that it was a gift.
How to spot it
Look for an inscription in the author's hand with words such as "with the author's compliments" or "from the author", sometimes with a date shortly after publication. Some publishers supplied authors with presentation copies bearing a slip or stamp. Provenance records, letters or a known recipient strengthen the case.
What it does to value
Presentation copies are usually more desirable than ordinary signed copies, because they come directly from the author, often at publication. When the recipient was important to the author, the copy is also an association copy and can be worth a great deal more. A presentation inscription to an unknown person still adds a premium over an unsigned copy.
See signed and inscribed books for the difference between signed, inscribed, presentation and association copies.