what is the difference?
He walked up to the door of his house.
He walked to the door of his house.
amirmkd.
There is no difference for most purposes.
This might be one subtle difference: "up to the door" means he definitely got as far as standing in front of the door, whereas in some circumstances "to the door" might mean "towards the door", which leaves open the possibility that he didn't get there. "He walked to the door of his house but before he reached the porch a shot rang out and he fell to the ground".
not a teacher
I agree with JMurray.
In addition, he might actually have to walk up to the door if it's on a higher level than the pavement or at the top of a sloping drive.
Rover
I agree with both JMurray and Rover. I, personally, feel that in JMurray's example, "He walked to the door of his house but before he reached the porch a shot rang out and he fell to the ground", most people would use 'towards' rather than 'to'.