It took until March 16 for a progressive voice to ask what the heck Cruz was talking about. At ThinkProgress, Judd Legum reported on a Cruz tweet—"We need to repeal every word of Common Core!"—with the headline "Ted Cruz Makes Impassioned Plea For Repeal Of Federal Legislation That Does Not Exist." Matter-of-factly, Legum explained that
"Common Core is not, in fact, a federal law," that
its standards were "developed by the states," and that the federal government played "no role" in writing them.
http://www.bloomberg.com/politics/articles/2015-03-19/what-ted-cruz-talks-about-when-he-talks-about-common-core In short, the standards are meant to get every student in America on the same page. Right now, the Common Core standards cover two areas: math and English language arts (writing and reading).
They were developed by a group of governors, chief state school officers and education experts from 48 states. To date, 44 states and the District of Columbia have formally adopted the new standards. By Spring of 2015, most of these states plan to administer state tests that have been aligned to the new standards.
http://www.npr.org/blogs/ed/2014/05/27/307755798/the-common-core-faq#q1