You may have noticed a small cylindrical canister or flat paper packet in your vitamin bottle that has a warning not to eat it. This is a desiccant pack and is put there to absorb moisture that is detrimental to your precious supplements. Moisture can destroy the chemical integrity of your supplements making them inactive.
Therefore you should keep the desiccant pack in the vitamin container.
However the desiccant can absorb only so much moisture and if exposed to excessive moisture will be rendered ineffective. Furthermore, it can itself become a source of moisture if it becomes saturated.
This is why it is important to avoid storing and opening your supplement bottles in moist environments like the bathroom or above a stove where water is boiled. This is also why it is not a good idea to store your supplements in the fridge since moisture will condense in the bottle if it is still cold when opened.
Always immediately put the cap securely back on the vitamin bottle after removing the pills you are going to take to avoid prolonged exposure to the air.
While you should leave the desiccant in the bottle you should remove the cotton plug at the top of the bottle since it will attract moisture.
Buying very large containers of supplements may be economical and convenient but you risk the likelihood of them degrading over time due to exposure to light, heat, air and moisture.