The issues specific to Arizona have to do with the proximity to Mexico, and the large land border that they share. The southern border of Arizona is largely desert and sparsely populated. There are no sizable population centers on either side of the border for hundreds of miles. The fact that the southern border of Arizona is merely a political boundary, not following any natural land formations or rivers, makes the boundary hard to distinguish from the ground.
As a result, the area is used for illegal entry into the United States from Mexico. The large land area provides miles of open space to cross without regular patrols to guard the border. In the 1990's, an estimated 80,000 people who had come across the border illegally were estimated to be living in Arizona. By 2010, that number had risen to nearly half-a-million.
The concern to the Arizona state government was the lack of action taken by the federal law enforcement agencies. Whatever the reasons were for the lack of federal action, Arizona wanted to have the ability to assist the federal agencies by using their own state law enforcement personnel in handling immigration issues. To do this, they needed to have a law passed at the state level. The law was introduced in the state senate as SB 1070, and became known as Arizona SB 1070.
The legal challenges to the law included a law suit by the Attorney General of the United States that ended up being heard by the Supreme Court. In a 5-3 decision, parts of the law were upheld, and other parts were deemed to be preempted by the federal law. By upholding parts of the state law, the state law enforcers in Arizona can request legal documents while interrogating persons suspected of breaking the law.
Ultimately, the question of state sovereignty on enforcement of immigration issues was not strengthened nor weakened by the Supreme Court decision. Arizona law enforcers can be involved with immigration issues to a certain extent, and that was the initial intent of the passing the law. Creating an environment where everyone in the state has legal status and every person is judged according to the law will take a longer period of time to accomplish.