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.