The theory is that there is a community, whose members speak "a language" (one language). They go about life, roaming the plains of whatever, and their children learn that language. As long as they remain a coherent community whose members are in contact with one another, everybody speaks the same language. The language might change a bit, but it changes for everybody. But sometimes one group of people head off somewhere else, and have little to no contact with their cousins. Languages change all the time, but when you have a single community whose members are in contact, the change tends to be in the same direction. Once you put a mountain or other obstacle between two communities, the speech of one group can become substantially different from the speech of the other group. Initially, that might be called (by linguists) a difference of "dialect", but with enough time and change, you have different languages. The "proto-language" is the language as it was spoken by a single community, and the "descendant languages" that are used to reconstruct the proto-language are the languages that you actually encounter.
Obviously, contact and social influence are not an all or nothing proposition. Suppose that humans shipped 10,000 people to colonize a planet in another galaxy. Even if everybody used English, not everybody in this community would speak the same dialect of English. Some would be from California, some from New York, some from South Africa (and so on), and some would be second-language speakers from France or Mongolia. One or two Mongolian speakers would probably not have a substantial impact on the resulting language 2,000 years after, but if the Mongolian community were 1/3 of the population, there is a fair change that that would have an influence on later languages. There would already exist dialects of English, and distinctions could be passed on depending on whether your ancestors were from the Mongolian-influenced dialect vs. the California-influenced dialect. Hence the assumption that "Proto-Indo-European" or some other language was originally completely homogenous is likely to be false.