The Minion method is a way to keep a barbecue fire going at a low temperature for an extremely long period of time. It was invented for use in bullet-style smokers. The inventor, Jim Minion of Seattle, found that his Weber Smoky Mountain could not cook at less than 300 degrees! This is too hot for most barbecue, so Minion invented a way to burn longer at a much lower temperature. It's very simple: don't light all the charcoal at once.
Originally, Minion loaded his cooker with unlit charcoal briquettes (which burn longer than lump charcoal). He then lit about 20 more briquettes and placed them atop the unlit pile. Over the next 18 hours, this unlit charcoal gradually caught fire, allowing a long cook at low temperature without requiring additional fuel.
This method has become popular among barbecue enthusiasts with all manner of equipment. Some styles of cooker require a slight modification to Minion, as the charcoal needs to be packed in one place so that it will all catch. In particular, an offset smoker requires a rectangular charcoal basket to avoid briquettes spilling all over the place.