Fetching details from the dictionary...

to pin down; to hold down; to press down; to hold in place; to hold steady
to cover (esp. a part of one's body with one's hand); to clutch (a body part in pain); to press (a body part)
to get a hold of; to obtain; to seize; to catch; to arrest
to grasp (a point); to comprehend
to quell; to subdue; to suppress; to repress; to hold back; to check; to curb; to contain
風で飛びそうな紙を手で押さえた。
I held down the paper that was about to blow away.
大事なポイントを押さえておこう。
Let's grasp the important points.
出費を押さえるために自炊している。
I cook for myself to keep expenses down.