Common Core means federal control of school curriculum, i.e., control by Obama administration left-wing bureaucrats. Federal control will replace all curriculum decisions by state and local school boards, state legislatures, parents and even Congress because Obama bypassed Congress by using $4 billion of Stimulus money to promote Common Core.
It's not only public schools that must obey the fed's dictates. Common Core will control the curriculum of charter schools, private schools, religious schools, Catholic schools and homeschooling.
The control mechanism is the tests. Kids must pass the tests in order to get a high school diploma, admittance to college or a GED. If they haven't studied a curriculum based on Common Core, they won't score well on the tests.
Common Core cannot be described as voluntary. Since CC is so costly to the states (estimated at $15 billion for each state for retraining teachers and purchase of computers for all kids to take the tests), CC is foisted on the locals by a combination of bribes, federal handouts, and as the price for getting a waiver to exempt a state from other obnoxious mandates, such as No Child Left Behind.