I've heard people ask the question: why couldn't he have just cast different actors for each age of the kids? He could have, but it wouldn't have been the same film. By using the same actors, I like to think that the characters' themselves grew up over time just as we all do. Sure you can dress up a 40-year-old man in 80-year-old make up and have him act like an 80-year-old and he might do an incredible job of it. That's what actors do. But to film the man at age 40 and then again at age 80 is to add a layer to the character that wouldn't be there otherwise.
Actors inevitably bring a part of themselves into a role. In Boyhood, the fact that the child actors, Ellar Coltrane and Lorelai Linklater, who played Mason's older sister, Samantha, are the same age as their characters makes it more naturalistic. The actors don't have to work so hard to play a certain age; they just focus on the character, a character that they've grown accustomed to over several years, a character that has had the time to grow up like an actual child does.
All of this naturalism lends itself to Linklater's goal, which seems to be to show his audiences how everyone has to grow up. We all have different stories, different plot lines, but we share a common experience in the path from childhood to adulthood: we learn, we adapt, we grow, and one day, we're adults. It gives me somewhat of a sense of unity with others, but more than that, watching Boyhood gives me a sense that we're all going to be okay because there is always a next step; there is always a future.