Of the reforms that took place in America during the nineteenth century, which one was most important? What issues did the reform raise, and how did it affect American society?

This is a big question, and also a matter of opinion. I would argue, though, that the biggest reform of the nineteenth century was the abolition of slavery with the Thirteenth Amendment. More than anything else, the emancipation of an entire class of enslaved people did more to change American society than anything else at the time.
Ever since the founding of the United States, the country had been deeply divided over the issue of slavery. Tensions finally came to a head in 1861 when the country descended into a bloody civil war over the issue. Even with a Northern victory, emancipation was not a certainty until the passage of the Thirteenth Amendment.
About four million former slaves received free legal status. Politically, this changed the way Southern states would be represented in Congress and in the electoral college. The Constitution had previously counted a slave as three-fifths of a person for the purpose of population-based representation. As free people, they now were counted equally with others. This dramatically changed the number of representatives awarded to the South after the 1870 census. Northern Republicans were concerned that this would be damaging to their party. As a result, Republicans began to heavily court the favor of former slaves. One thing they did was set up the federal Freedman's Bureau to help former slaves adjust to a life of liberty.
The effect on society could be most deeply felt in the South. Many large plantations lost a significant amount of their labor force as emancipated slaves left for other opportunities. However, the old plantation style of farming did not end with emancipation; it merely adapted. Sharecropping became a widespread form of employment for black people in the South. In many ways, this system of using tenant farmers recreated the conditions of slavery by keeping the black tenants bound to the land.
Furthermore, racism did not end with the Thirteenth Amendment. In some ways, it only intensified. "Black Codes," laws designed to criminalize many aspects of black life, abounded in the South. These state-level laws applied exclusively to the African American population and made it easy for local law enforcement to circumvent the Thirteenth Amendment in order to persecute African Americans, imprison them, and subject them to forced labor.
So, while the reforms brought about by the emancipation of slavery had limited immediate effects, I would argue that it was still one of the most significant reforms of the era. The following two Constitutional amendments and several other federal reforms sought to empower a large population of former slaves. The hope among many reformers was that African Americans would be able to participate fully in American society. The pushback they received was massive, and more than a century would follow in which freed slaves and their descendants would struggle to achieve the full freedoms that these earlier reforms promised.
https://books.google.com.ni/books?id=VMCXjRyyKTQC&pg=PA46&dq=thirteenth+amendment+%22three+fifths%22&redir_esc=y&hl=es-419

https://www.archives.gov/historical-docs/13th-amendment