"Corkage fee," sometimes called a "cork charge," refers to the charge imposed by a restaurant for every bottle of liquor served that's not bought directly from the restaurant. In other words, if you bring in your own bottle(s) of wine or alchohol, the restaurant assesses a fee for opening it and serving it to you. This fee pays for the rental of the glasses and the service you receive.
Also, some restaurants that don't have a liquor license will allow you to bring in your own alcohol and do or don't charge you for the privilege.
Possibly it should be called an "uncorkage fee," except that in many jurisdictions, the restaurant must re-cork the remaining wine before allowing you to take it off the premises.
The corkage fee is usually $5-$20 a bottle, depending on the restaurant, and whether or not the bottles you bring in are sold by the restaurant itself. Some restaurants charge a lower fee if the patron's wine is not on its wine list -- for example, with an older or particularly distinctive wine.
A quick call to the restaurant will confirm the amount of the corkage fee.
Some restaurants advertise that they don't charge a corkage fee. In Las Vegas in 2003, we covered the Pinot Brasserie at the Venetian, which made a promotion out of suspending its cork charge. We brought in three bottles to test the claim.
Here's what we wrote:
"This isn’t one of those promotions that management advertises, but the staff doesn’t support. The waiters brought glasses, opened the wines, and were attentive to pouring throughout dinner. There are no restrictions on what you bring or how much; carry in a couple bottles of Dom if you like. The saving for bringing your own at no charge is significant and provides budget flexibility to enjoy the best Pinot has to offer."
If you check out our Restaurant listings, you'll find that we list the corkage fee for many restaurants (although we confess that it's been awhile since we updated that data, so it's a good idea to call in advance and make sure that they still offer the service and haven't upped the price since we last checked).