The phrase suggests a metaphorical rise in social standing, similar to climbing a ladder. He really came up in the world after marrying the CEO's daughter.
Pro Tip 2/3
Not Literal
The phrase doesn't refer to physical movement, but to social or financial improvement. After years of hard work, she had come up in the world.
Pro Tip 3/3
Potential Irony
Can be used ironically if someone's effort to improve status has clearly failed. Bought a fancy car to come up in the world, yet he's still living in his parent's basement.