In general, the term breaker bar refers to a length of pipe or metal used for leverage. A breaker bar can be anything from a simple length of metal pipe to an extra-long manufactured ratchet driver, the latter being a much safer and effective method. It serves a variety of purposes, but the most common function is freeing--or "breaking"-- stuck bolts using extra leverage and torque to turn the threaded bolt.
A breaker bar allows the user to take advantage of extra leverage supplied by a longer tool while still applying the same amount of force to the tool. For example, by slipping a length of pipe over the end of a ratchet, the user can apply extra leverage to the tool through the breaker bar, thereby putting more force on a stuck or rusted bolt. This process of using an extra piece of pipe slipped over a ratchet is sometimes called using a cheater bar. While this method can work well, be forewarned that this process may cause the tool to fail catastrophically; applying extra force to the ratchet mechanism may cause it to slip, thereby risking damage to both the tool and the bolt, as well as to the user. To solve this problem, manufacturers produce breaker bars without a ratcheting mechanism on them; this applies more force directly to the socket and to the bolt, rather than to flex from the ratcheting mechanism.
Many tool manufacturers produce a ratchet breaker bar as well, which is simply a ratchet driver with an extra-long handle. This type of breaker bar eliminates the need for a second piece of material, thereby reducing the likelihood of the tool slipping, which can cause damage to the tool and bolt, and injury to the user. However, extra force placed on the ratchet mechanism is still a risk, so the best breaker bar option is the non-ratcheting design mentioned above.
Some common applications for a breaker bar include freeing lug nuts on car tires, freeing a variety of bolts in car repair and maintenance--where rust is a common problem, thereby causing many instances of stuck bolts--manufacturing applications, home renovating projects, and any other instance in which a bolt has become frozen in place. A breaker bar is a good investment to work in conjunction with a ratchet set, however big or small. They are generally inexpensive for a simple model, but higher end, ratcheting models could cost significantly more.