Tarragon is widely used in classic French cooking for a variety of dishes including chicken, fish, and vegetables, as well as many sauces, the best known being bearnaise (a distinctive and classic French sauce). It's also an integral ingredient in a variety of herbal combinations, including fines herbes; other herbs included in this classic combination are chervil, chives, and parsley.
Tarragon's flavor is strong, so it can overpower other flavors and should be used with a light hand. Also, cooking intensifies the flavor of both fresh and dried tarragon.
Some gourmet markets carry tarragon vinegar, which works well over salads of fresh leafy greens.