First of all, you should be aware that there were actually three Reconstruction Acts passed in that year. Together, the effect of these laws was to impose martial law on the South in an attempt to force them to institute new and more democratic governments.
The Reconstruction Acts abolished the state governments in the South and replaced them with military governments. The military governments were instructed to do various things. They were supposed to call conventions for making new state constitutions, for example. They were supposed to ensure that freed slaves (male only) had the right to vote. In general, they were supposed to ensure that new state governments would be made on the basis of universal male suffrage and a respect for the rights of all citizens.