Bitters is an aromatic liquid distilled from herbs, roots and barks of various plants. Bitters was used for "medicinal" purposes as well as an additive to various beverages. The most common brand in the U.S. is Angostura bitters. Bitters do have a high alcohol content. Due to their potency bitters are typically used in very small quantities. Another popular brand is Peychaud's.
Bitters are commonly used in an Old Fashioned, Manhattan, and Mai Tai?
You can purchase bitters in any liquor store, or any store that sells alcoholic beverages. Although Angostura bitters is the "go to" brand there are now hundreds of boutique bitters available. Because the formulations can be very different they can't necessarily be use interchangeably. You can purchase Angostura bitters online at Amazon.com:Angostura Aromatic Bitters. You can also purchase a "set" of the most popular bitters here: Bitters Variety 3-Pack: Angostura, Peychauds and Regans.
If you don't have Angostura bitters you can substitute: