to go up, or to go towards the top of something:
The plane climbed quickly to a height of 30,000 feet.
As it leaves the village, the road climbs steeply up the mountain.
The sun climbed higher in the sky.
to use your legs, or your legs and hands, to go up or onto the top of something:
to climb the stairs/mountain
I hate climbing ladders.
We're going climbing (= climbing mountains as a sport) in Scotland next weekend.
If a price, number, or amount climbs, it increases:
Our costs have climbed rapidly in the last few years.
to move into a higher social position, or to improve your position at work:
He quickly climbed to the top of his profession.