Run in and breaks are generally performed by fast jets returning to the circuit, and they represent the quickest and most fuel and time efficient way of transitting back for a landing.
They also represent the easiest way to bring a formation into the circuit. This allows one aircraft at a time to peel off into the downwind. Straight in approaches take a great deal longer, and use more fuel with formation handling a lot more sloppy at low speeds (ie under 200 kts.)
The run and break allows a circuit join to be performed with the minimum of hassle, whilst saving time and fuel. A downwind join, for example, may cause other problems with the speed differnces in aircraft. A fast jet maybe downwind with no less than 160 kts, a C152 with 65kts(?) Problem self explanatory.
Of course due to its nature, the manoeuvre can only be performed if the circuit traffic allows it. The lead aircraft is responsible for positioning and if a run and break is attempted to a full circuit then that is a bad call and questionable airmanship.
Stiknruda's explanation is pretty accurate although initials is normally at 3-5 nm and heights vary according to aircraft type and local SOPs.
Aside from all this they're awesome fun and basically the only way to return from a trip, if you don't mess anyone else up in the process!!
Regards
