The most popular dish is the "asado", it's kind of a barbecue in which you roast most of the parts of the cow, not just the common meat. It's also usual to eat "picada" (small dishes of cheese, salami, olives, peanuts and french frites or other similar ingredients) before the asado.
A traditional drink is "mate", an infusion made with a plant called "yerba mate". People drink it with a tube for sipping in a recipient also called "mate". It can be made of gourd, wood or even bull hoof. It's a custom to share the recipient by many people and they don't mind sharing saliva.
The sweet delight par excellence is "dulce de leche", a candy made of milk and sugar with a really special flavour, eaten by kids and grown-ups.
More information: http://www.argentour.com/en/argentina/argentina_food.php