When you have a space with anything more than one dimension, all senses of direction become a matter of perspective.
The only way to make a definitive statement about direction is if it is relative to yourself, and your perspective on the universe. People can, and usually do say something like "it's on my left", or "on your right."
People generally accept, incorrectly, that "Up" and "Down" are not able to be argued. Remember, that what is "Down" to people in the Arctic, is "Up" to people in the Antarctic. The reverse applies as well. It is implied earlier in this node that "Up" is away from the Earth. This is again, relative to individual perspective. "Up" at the Equator could be "left", "right", "forward", or "backward" to someone in the Arctic or the Antarctic, depending on their position.
And of course, there are the axes: X, Y, and Z. Unfortunately, these are again, relative to our planet. Since our planet is not a plane, X, Y, and Z can't be practically applied.
For the sake of argument, let's assume an alien ship is flying toward Earth. They are parallel to what we refer to as the Z axis (Up and Down, for the uninformed.) When they reach Earth, the front of their ship points at the Arctic.
Now, are they above us, pointing downward? Or are we ahead of them? Both, and neither. Each answer is correct and incorrect, depending on your perspective. If you are aboard the alien ship, this big blue ball is in front of you. If you are on Earth, this ship is pointed down, hovering above your planet.
Take a look at some works by M.C. Escher, especially his work titled "Relativity." Study it from lots of different angles, then try to decide which person is oriented correctly.