Intuition about Hubble's Law
Think about it as if you were baking bread (or cake, whatever you prefer). When you bake a bread with raisins, it rises in all directions (due to the yeast). Every raisin in a rising loaf of raisin bread will see every other raisin expanding away from it. Now suppose the raisins as galaxies and the yeast as the Hubble constant.
An illustration from Hyperphysics (Georgia State University) to illustrate this further:

When you now suppose you are the raisin at the edge, from your perspective, you are standing still and the other raisins are receding away. It is all about the perspective, the body which you take as a reference (like with relativity).