Tartines are just a french way of saying "openfaced sandwich".
They are made on a large slice of toasted hearty bread and usually have something warm and melty on in. Ina Garten has some great ideas: try the eggsalad smoked salmon one for starters. This was my tartine in a cafe in Avignon: melted mozzerella with tomatoes, olives and anchovies with a light salad. A perfect lunch.