Use tomorrow to describe the day after today. If it's Monday, and you tell your brother that you'll see him tomorrow that means you'll see him on Tuesday.
Tomorrow can also mean "the near future." When someone says, "Children are tomorrow's leaders," it means fairly soon, not "when they wake up in the morning." Speaking of morning, the Old English word morgen means "morrow or morning," so tomorrow means "to morning." The morning that follows today is always tomorrow.
