Each government funding program has its own set of guidelines, and there are some that are allocated specifically for minorities. The definition of what constitutes a minority differs a little from place to place, but it will typically be defined in the program guidelines.
The idea behind providing funding that is earmarked for minority members of our society is an acknowledgement that there may be (or was in the past) unequal treatment and limited opportunities. Even when everyone does start getting treated more fairly, some sociologists observe that the disadvantages can extend further for another generation or more, possibly because of residual ideas and attitudes that younger people may still experience.
Until the point is reached when everyone is on equal footing, whether from internal sense of capability or external opportunities, grant funding for minorities is a tool that is used to help reach that point. Some examples of the funding that is available are scholarships for minorities, educational grants for minorities, government grants for women to study in a male-dominated field or to start a business, grant funding for a professional degree (such as law or medicine), and much more.
Of course, the ideal situation is for every member of our society to have the maximum chance to succeed at a personal level, but until then, government grants for minorities are a way to equalize the opportunities in the meantime.