The 14th Amendment punished the South in a few ways.
The first major provision is this:
No person shall be a Senator or Representative in Congress, or elector of President and Vice President, or hold any office, civil or military, under the United States, or under any state, who, having previously taken an oath, as a member of Congress, or as an officer of the United States, or as a member of any state legislature, or as an executive or judicial officer of any state, to support the Constitution of the United States, shall have engaged in insurrection or rebellion against the same, or given aid or comfort to the enemies thereof. But Congress may by a vote of two-thirds of each House, remove such disability.
This provision keeps former Confederates from being in Congress, unless they are approved by Congress with a 2/3rds vote.
The second is this:
No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws
This is the Federal government telling the States that while they may have once had all the power in terms of setting rules around due process and how laws are applied to citizens, that is no longer the case. That privilege was lost with the Civil War and the Federal government will now be ensuring compliance and enforcing equal protection.
Finally, there is this: The validity of the public debt of the United States, authorized by law, including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion, shall not be questioned. But neither the United States nor any state shall assume or pay any debt or obligation incurred in aid of insurrection or rebellion against the United States, or any claim for the loss or emancipation of any slave; but all such debts, obligations and claims shall be held illegal and void.
This is saying that the states rejoining the Union have to help pay for the war debt of the Union but that there will be no aid in helping pay for the Confederates war debt and any claims about loss of property from Southern states, especially due to emancipation, are void.