The color change serves to immediately alert the viewer to the time jump. Generally it is the past that is shown without color, however since moments in the past are predominant in the series doing so would make viewing annoying. The lack of color highlights the fact that Saul's quality of life has declined (in a sense it is as if he is traveling backward from success to failure) and that he has had to suppress his bursting personality, which gives a depressed flavor to the scenes. Maybe when Saul makes his personality re-emerge with his flamboyant clothes and maybe he meets Kim again the colors will reappear, that would be amazing.
As noted by @aleppke in the comments, black and white is also used to maintain stylistic consistency with Breaking Bad, where in the second season this technique had already been used to depict future events.