The Reconstruction Era in the United States created a legal framework that made African Americans legally equal to white Americans. However, it also created a system in which those legal rights were taken away from blacks and segregation and discrimination were put in their place. This is how Reconstruction led to the Civil Rights Era.
The Reconstruction Amendments to the Constitution made blacks and whites officially equal. However, things like the literacy tests and the Jim Crow laws made a mockery of this equality. By the 1950s, African Americans and some whites were determined to do something to make the US live up to the words of the amendments that were passed during Reconstruction.
Overall, then, Reconstruction put in place the expectation that blacks and whites should be equal. This eventually led to the Civil Rights Era in which people worked to make that expectation into a reality.