We probably had heard our teachers and parents a million times stressing the importance of waking up early. Many idioms and expressions came about to drive the message home.
However, almost no one bothers to explain why is it so important. Only after undergoing the negative effect of not waking up early does one appreciate the habit.
The explanation is easy; you have less distraction and interruptions earlier in the day. Many people wakes up late, thus cutting down the number of possible interruption. Emergencies - whether real important stuffs or urgent trivial things are also easier to handle since you'll have more time to deal with it.
So inversely, when you wake up late the chance of interruption is high plus it's difficult to deal with emergencies. Needless to say, that's a perfect combo to not getting anything done and ruining your day.