Yes, it should go back over the head of the penis (when you're not erect) to cover it. The meatus (head) is an internal organ (mucous membrane), just like a woman's clit (or like your eyeball), and the foreskin is like your eyelid (or a woman's clitoral hood).
Gently pull it back down to cover the head after bathing or masturbating. The meatus needs to be protected from rubbing against clothing etc. and the foreskin keeps it clean too.
Don't ever force it further than is comfortable to do so. Also, don't pull it back and clean with soap. If you want to clean underneath, just slide your foreskin back in the shower, rinse under the warm water, then slide it back. If you have any irritation or smegma buildup (i.e. from being too rough with it) a soak in the bath will do wonders.