How it works
Age is broken into whole years, then whole months since the last birthday, then remaining days — the same way a person counts age by hand. This correctly handles months of different lengths, so counting from January 31st does not accidentally skip or duplicate a day.
Why the total day count is also shown
Years and months give an intuitive sense of age, but the total number of days is useful for its own reasons — checking eligibility rules stated in days, or just marking a round number of days alive.
Dates are read as calendar days
Both dates are treated as calendar dates with no time of day attached, so the result does not depend on which timezone your browser is set to.