What does breaking the marbel ceiling mean?

Answer 1

This expression was created in 2007 by the first woman Speaker of the US House of Representatives, Nancy Pelosi. It was her way of expressing that for far too long, certain people (women, minorities, members of the lower socioeconomic classes) had been prevented, due to discrimination, from moving into the top-most levels of government. Now that Rep. Pelosi had attained this important position, that barrier was finally broken.

Answer 2

In some circles the term of breaking the marble ceiling is meant that peoples underneath this imaginary ceiling could break through ans have access to political power. With that said, the term of "glass ceiling" serves that purpose better. One can see what's "above them" and it is a goal to break through. This would cover power in salaries and political power.