Most uses of the word understand it as referring to a middle ground on a spectrum between rejection, intolerance, hate, and persecution on one end, and acceptance, approval, love, and respect on the other. They distinguish it from indifference because it only comes into play when something is disliked or disapproved and matters.
Who is doing the tolerating, who or what is being tolerated, and exactly what such toleration entails can vary enormously. Individuals can be said to tolerate their own personal foibles, not to tolerate fools, or to tolerate whole groups. Groups can be said to tolerate individuals within or without, or other groups. States and other political authorities can be said to tolerate individuals, groups, or other states. That which is tolerated can range from the very existence to the appearance, ideas, or activities of the tolerated entity. Toleration can range from providing only limited encouragement, to doing nothing, to applying limited sanctions short of persecution.
Some authors have tried to distinguish "toleration" from "tolerance," with the former referring to official policies and the latter to a personal attribute, but ordinary language does not seem to distinguish the two. For example, we can say that the behavior of tolerant persons shows that they tolerate others, or that all we are asking for from another person is toleration. We can also say that a government policy reflects tolerance of some activity.
Some authors have thought that toleration is only a second-best, half-way measure, and that we ought to go beyond toleration to embrace and respect others. This is certainly the right thing to do where whatever is being tolerated actually deserves to be embraced. But one can wonder if all human beings really are always doing things that deserve respect. What would the world be like if all people and all of their activities were worthy of embrace? Certainly unlike anything we have seen so far. Then, perhaps, there would be no need for a concept like toleration. But until that moment arrives, this is the term for the response to things that merit neither active persecution nor full acceptance.
Toleration may look weak and thin from the perspective of a possible acceptance and embrace, but it can look very good from the perspective of someone who is undergoing persecution. Many a victim of intolerance would just like to be left alone, and that is one of the modes of toleration. One of the paradoxes of toleration is that if one is tolerant of everything, then one is also tolerant of the intolerant. This may mean complicity with persecution, or at least failure to prevent it.