The Logistic function models a situation in which a quantity changes slowly at first, picks up speed, and then slows down. 
Think about using a technology such as cell phones -- there are the early adopters, then the idea takes off, but eventually the number of new cell phone users slows down since almost everyone already has one. 
The following data is for the likelihood of getting breast cancer in the next ten years as a function of one’s age

bc={{20,0.05},{30,0.43},{40,1.43},{50,2.51},{60,3.51},{70,3.88}}