Carpaccio (pronounced "car-PAH-chee-oh") is a traditional Italian appetizer consisting of raw beef sliced paper-thin, drizzled with olive oil and lemon juice, and finished with capers and onions.
In contemporary cuisine, carpaccio can refer to any thinly sliced raw meat or fish, such as tuna, served in this fashion. Even thinly sliced vegetables or fruits are sometimes served as carpaccio.
There are a couple ways of making carpaccio. For beef, which is the usual type, you would start with a beef sirloin or tenderloin. Trim all the fat off of it. Even though the whole point of carpaccio is that it's raw meat, some chefs will sear the meat on all sides, just to give it a bit more flavor. But this isn't necessary or even all that common.
The next step would be to season the meat with salt and pepper, chopped fresh herbs and maybe a bit of balsamic vinegar before wrapping it with plastic and chilling it for at least 8 hours.
Finally, the meat is sliced very thinly. It's possible to do this by hand if you have a very sharp knife and excellent knife skills. But more likely, an electric meat slicer would be the way to go. It can help to chill the meat in a freezer for 30 minutes or so before slicing. You don't want it frozen solid — but just enough to make the meat easier to slice.
Beef carpaccio is usually served with capers, onions, olive oil and lemon juice, along with possibly some shaved parmesan cheese and chopped fresh parsley.
Note that some recipes will call for the meat to be pounded thinly, which is another way of doing it, especially with a lesser cut of meat, but the preferred technique is to use a good cut of beef and slice thinly.
Interestingly, carpaccio is named after an Italian painter who was known for employing bright red in his works, of which the bright red of the raw beef is reminiscent.