The child tax credit as I understand it simply expands the existing 1000.00 child tax deduction parents can claim on their taxes. It essentially lowers your taxable income if you have children. The savings component is a way for parents to set aside money for expenses like education, without being taxed on their earnings. It's similar to a Roth IRA, where the taxes are deferred until or unless you withdraw the savings.
This is why the controlled opposition on here is crying.