Educational opportunities expanded after the Civil War because the government set up more and more public schools.  This was done partly out of a desire to "Americanize" the children of the immigrants who were coming into the US in large numbers starting in 1880.  In part, though, it was also done because of the idea that educated people were needed for a democratic society to exist.

After 1870 in particular, public education took off.  The number of teaching colleges ("normal schools") went from 12 in 1860 to over 300 in 1910.  (Source: Bailey, et al. The American Pageant 11th Ed. p. 580.)  In 1870, 57% of school age children in the United States went to school.  By 1920, even with the influx of immigrants, that number was 78%.  (Source: Tindall and Shi, America: A Narrative History 5th Ed. p. 948).

Educational opportunities expanded, then, as governments set up more public schools after the Civil War.

How did educational opportunities change after the Civil War, and for whom?

After the Civil War ended, educational opportunities changed significantly for African-Americans. Before the Civil War, African-Americans who were enslaved in the South had no real opportunity to be formally educated. While some slaves were secretly taught how to read, write, and compute, there was no formal schooling for the slaves. There also was a significant risk in trying to get an education while being enslaved.

After the Civil War ended, things changed for African-Americans regarding educational opportunities. The Freedmen’s Bureau was created to help African-Americans adjust to freedom. One thing that the agency did was to help African-Americans establish schools. The Freedmen’s Bureau helped to provide the funding for these schools. Teachers were hired and school buildings were constructed. Additionally, colleges were established for African-Americans. As more African-Americans became educated, they had more people who could teach in these schools. Reconstruction was very important for helping start the process of educating African-Americans after the Civil War ended.