We know that there is a huge amount of atmospheric pressure on us but we do not experience its effect. Why?
There is a huge amount of atmospheric pressure on us but we do not experience its effect because the same amount of pressure is exerted outwards through the fluids in our body cancelling the atmospheric pressure.
You can feel pressure if your body is not in equilibrium with the surrounding air. This happens if you drive down a mountain too fast; you have to pop your ears. It's also a big problem with diving underwater because all that's needed to be at twice atmospheric pressure is to dive down to 33 feet. Come up too fast and you'll feel a good deal of pain, and possibly sustain some damage. Come up slowly and your internal pressure will have time to keep pace with the changes in pressure.