"Yakiniku" refers to all grilled meat, but when Japanese people say, "Let's go and eat yakiniku", it usually refers to barbecuing meat and vegetables on a net or iron plate, then dipping them into sauce and eating them.

Here are the parts of beef good to know for when you order at a yakiniku restaurant.
Karubi (Galbi) is short ribs of beef and pork(usually served without bone), and is fatty. It is the standard part of meat that most people order.
Tan (tongue) is beef's tongue, it has a rich taste with less fat. The more you chew, the more flavor comes out.
Harami (diaphragm) has lean meat, known for being a healthy part of the meat and popular among female customers.
Liver is beef liver and is rich in iron but has a distinctive smell and taste and many people dislike it.
Horumon (offal) is beef's large intestine and its shape is mostly round. It has a rich fatty taste and chewy texture.

After you barbecue the meat, it is generally eaten with a dipping sauce. The sauce is soy sauce-based seasoned with garlic, sugar and sesame oil. The taste is different in each restaurant. There are usually a spicy type and sweet type of sauce.

Mostly people eat yakiniku with others, but recently in Japan, there are places where you can enjoy eating yakiniku alone.