To move up in the hierarchy of a corporation.

A 'ladder' is a device with steps used to 'climb' (or move) up and down, so the 'corporate ladder' is the series of steps people go through as they gain more power in a corporation and 'rise to the top' - from file clerk up to president.
You have to work very hard if you want to climb the corporate ladder.
by VAKI5 May 12, 2005
This pharse refers to moving up in rank within a particular field or business. If someone "climbs the corporate ladder" to the top, they started out at the bottom (stockboy, mail clerk, etc) and ended up at the top (CEO, CFO, vice pres., etc.)
Tim lived the American Dream. He started out as a desk clerk and climbed the corporate ladder to the top. He is now a CEO in the same field that he had started out in.
by Doobie Smokes You December 12, 2004