bal·sam·ic vin·e·gar

noun: balsamic vinegar; plural noun: balsamic vinegars
  1. dark, sweet Italian vinegar that has been matured in wooden barrels.
Balsamic vinegar is a vinegar originating from Italy, increasingly popular throughout the world. The original, costly, traditional balsamic vinegar, is made from a reduction of cooked white Trebbiano grape juice, and used as a condiment. 

Balsamic vinegar = aceto balsamico = aceto di balsamico Pronunciation: ball-SAHM-ick
 
Notes: This enormously popular Italian vinegar is prized for its sweet, fruity flavor and mild acidity. It's terrific for deglazing pans, dressing salads and vegetable dishes, and for seasoning everything from grilled meat to poached fruit. Its quality varies enormously. Expensive artisan-made balsamic vinegars (labeled traditional or tradizionale) are aged in wood barrels for at least 12 years and can cost over $100 per bottle. They're exquisitely complex, syrupy and only slightly acidic. Those who can afford them often drink them as they would a vintage port, or use them in desserts, where their sweetness and subtleties can be shown off to best advantage. Cheaper commercial brands are watered down with wine vinegar and artificially colored, but they're fine for most recipes. 

Substitutes: brown rice vinegar OR Chinese black vinegar (cheaper) OR red wine vinegar + sugar or honey OR sherry vinegar OR fruit vinegar. 

For a more in-depth look at Balsamic Vinegar Read: Everything You Need to Know About Balsamic Vinegar.

Sources & References
Source: Wikipedia
Source: www.foodsubs.com