The Radical Republicans envisioned a radical new life for Black people, particularly in the South, following the Civil War. Most Republicans were against granting equal rights to Black Americans, which made this group's vision more radical than that of the typical Republican. They believed that Confederate leaders should be held accountable for their role in the war and that Black people deserved the same rights as white people. To this end, they created the Freedman's Bureau to protect former slaves in the South and elsewhere. Radical Republicans believed that former slaves had a place as active leaders in their communities, and they enlisted the assistance of the United States Army to occupy Southern states and help protect the newly freed slaves.
In order to understand Charles Sumner's remark, it's necessary to first look at the way the Bill of Rights was written. Note that these declarations reflect the expected limitations of the federal government. It "shall make no law" and "shall not ... violate" and "shall not require." The Bill of Rights had an intentional focus on limiting the powers and interventions of government in state matters. Yet in the Fourteenth Amendment, a shift in the purpose of the federal government, is reflected in the words found in section 5: "Congress shall have the power to enforce." Charles Sumner therefore commented that the federal government had to serve as the "Custodian of Freedom" in order to establish a national consciousness that was inclusive of all based on birthright and regardless of race. Instead of limiting the power of the federal government in states' affairs, this amendment bolstered its influence.