Jack Johnson's career was at its peak from 1908 to 1914, which offers a clue as to why he is such a significant fighter. Johnson was black. There was never a black world champion before him, because white fighters refused to fight against black men. When he finally got his chance and won, he endured all the bitter, racist hatred the world could muster, and eventually lost the title in a match he claimed he threw.
There is no single sanctioning or governing body recognized worldwide as the "primary" boxing association. The influence held by the WBA, WBO, WBC and IBF varies regionally and may be superseded by a local governing body, such as the British Boxing Board of Control (BBBC) or the Nevada State Athletic Commission (NSAC). However, these local groups and state regulatory boards usually have a set of regulations that the other governing bodies must follow while in their territory, but don't publish rankings of their own. There are also dozens of other, smaller boxing organizations worldwide.
So how does a boxer get a chance to fight for the title? He has to work his way up through the ranks. A boxing organization publishes monthly rankings of their top boxers. The current champion in the weight division is listed at the top, and then the contenders are listed. A boxer moves through the ranks by fighting progressively tougher opponents. The rankings are influenced by a boxer's win-loss record, the difficulty of the opponents he's beaten, and how convincing his victories were.
The top contenders have a chance to challenge for the championship. The current title holder is obligated by the organization to defend his belt on a regular basis. This can range from once every nine months to once every year. If one contender stands out above the rest, the current title holder (the defender) and the contender must negotiate the terms of the fight (actually, their managers and the fight promoter take care of this). If several contenders seem like they all have an equal shot at the title, they will fight each other in a series of elimination matches held over the course of several months to determine one true challenger for the title.