The 15th Amendment gave African American men the right to vote (women still could not vote yet). As a result, the South tried to prevent them from voting by creating the Grandfather Clause, part of a law they passed which created literacy tests and poll taxes as a requirement to vote. The majority of African Americans during this time were illiterate (could not read or write) so they were unable to vote. Since African Americans were just freed from slavery, they were poor and barely had money, so they could not pay poll taxes.
I'm not so sure about this next part though so maybe you'll want to skip it and ask your teacher:
There was also a rule that said people whose Grandparents could not vote also could not vote. Since all African Americans' grandparents were slaves and could not vote, then none of them could vote.
