To add to the dictionary definition Alenanno provides, I feel obliged to point out that the expression "fresh out of" is a colloquialism that is often used in a confrontational manner. In the film Full Metal Jacket, for instance, the belligerent Marine called "Animal Mother" confronts the film's protagonist, Private Joker, by saying: "Hey, asshole. Cowboy's wasted. You're fresh out of friends."
There are other kinds of confrontational usages, sometimes implying that the speaker is not really out of the item, just that he won't sell any to you. For example, if a black man in the South before the civil rights movement tried to buy something in a "whites only" store, he might have heard that usage in a mocking, derisive way:
Black customer: Can I buy some cigarettes here?
White proprietor: [Standing in front of shelves stocked with cigarettes] Boy, we're fresh out.
The other connotation is that the seller has just this minute run out of the item.
Do you have any blueberry pie?
Sorry, we're fresh out. The guy who came in just before you ordered the last piece.