The phrase implies that with knowledge or education one's potential or abilities in life will certainly increase.
Having and sharing knowledge is widely recognised as the basis for improving one's reputation and influence, thus power.
This phrase may also be used as a justification for a reluctance to share information when a person believes that withholding knowledge can deliver to that person some form of advantage.
Another possible meaning for this phrase can be found in philosophical idealism - if the world exists solely as the content of consciousness, then knowledge itself can be used to directly manipulate the content of reality.
http://en.wikipedia.org/wiki/Scientia_potentia_est