It is the most radical phrase in the Declaration of Independence: that government gets its power not from God or birth, but from the permission of the people it rules.
Consent of the governed is the principle that a government's authority is legitimate only because the people agree to be governed by it. Power flows up from the governed, not down from a king, a bloodline, or a deity.
For most of human history this was a fringe, even treasonous, idea. Kings ruled by divine right, claiming God had placed them above the people. To say a ruler needed the people's permission was to deny the entire basis of monarchy.
The Declaration of Independence made it American doctrine in 1776. Governments, Jefferson wrote, derive their just powers from the consent of the governed. The sentence quietly demolished the divine right of kings and put the people in charge of their own rulers.
It carries a sharp edge. If government depends on consent, then consent can be withdrawn. The same Declaration says that when a government becomes destructive of the people's rights, it is the right of the people to alter or to abolish it.