According to an elementary textbook the New English File (starting with chapter 3/B daily routine) your day starts when you wake up and ends when you go to bed.<br>
But yes, what people mean in real life depends on the situation. On a job interview I wouldn't include the parts of my day that's not related to work but in a different situation, e.g. a journalist asking it, interpreting when your day starts and ends may depend on you.<br>
So generally speaking it does include all 24 hours of the day unless the question is about a specific part of the day or you have reason to interpret it as such.