1
general::
Seek protection, find a hiding place, as in It started to pour so we took cover under the trees, or He wanted to avoid the reporters so we said he could take cover in our summer cottage. This term uses cover in the sense of ‘‘shelter" or "concealment," a usage dating from the 1400s.
American Heritage Idioms
2
general::
Phrase(s): take cover
to seek shelter from gunfire or other projectiles. • As soon as the firing started, we took cover behind a huge boulder.
McGrawhill's American Idioms And Phrasal Verbs