It's called the "Legal Arizona Workers Act." It was passed in 2007, and went into effect in 2008. The law authorizes the state to suspend or "sanction" businesses through the state licensing policy, and also mandates business participation in the E-Verify system, contradicting federal rules maintaining E-Verify as a voluntary "experiment."

...the 2007 Legal Arizona Workers Act, commonly called the employer-sanctions law, which was among the first in which a state tried to assume control of what previously had been strictly a federal function. The landmark has withstood challenges in U.S. District Court and the 9th U.S. Circuit Court of Appeals, which have said the law is constitutional.

The act emboldened Maricopa County Sheriff Joe Arpaio, who unlike other sheriffs across the state has used it to conduct 40 raids on businesses accused of employing illegal immigrants. Those busts have resulted in 308 arrests for identity theft and forgery, while two employers have faced civil sanctions.

Supporters and opponents of the law agree the Supreme Court's ruling could have sweeping ramifications. If the law is upheld, other states likely would consider similar legislation. The ruling also could influence the future of Arizona's broader immigration legislation, Senate Bill 1070.

In U.S. Chamber of Commerce v. Whiting, et al. arguments for the state of Arizona center around a 1986 provision of Congress reinforcing a state's right to define and enforce business licensing as they see fit, and on the mandatory E-Verify aspect of the law, a claim that mandatory involvement of AZ businesses will only help text the effectiveness of E-Verify.

The Chamber of Commerce, joined by several civil rights legal defense organizations argue that the law is unconstitutional as a state level employment standard and mandatory enforcement of immigration law contradictory to federal provisions. SCOTUS Blog:

...the challengers’ brief belittled the notion that Arizona had simply enacted a “licensing” law, so it was protected by the exception Congress wrote into its scheme.  If all that is needed to make a law regulating alien employment a licensing law is that denial or revocation could occur at some point in the process, then, the challengers said,  “a state may regulate work-authorization status in whatever fashion it wishes — so long as, at the end of the day, something labeled a license may be affected.

What Congress meant by the exemption clause, the challengers insisted, was only that “states could rely on federal determinations of compliance with federal immigration laws when issuing business licenses or permits to farm labor contractors.”  The exemption clause, it added, “permits states to tack on certain sanctions in the form of the suspension, revocation or refusal to reissue a license for persons who have been found to have violated the sanctions provisions” that Congress had imposed, not those that a state might seek to impose.

This is going to be an important ruling, preempting the SCOTUS's look into Arizona's SB1070 next year.  The argument made by AZ over the "Legal Arizona Workers Act" amounts to a trial balloon for the argument they will make in defense of SB1070: Since the federal government hasn't acted, state must.  Basically, Arizona is arguing that a lack of action on the federal level regarding immigration law somehow, magically, inexplicably amounts to an automatic transfer of power to the states.

I doubt the SCOTUS will agree, what with that whole Constitution-Not-Hard-To-Read thing.

But due to a conflict of interest, Kagan -- who reviewed the preliminary challenges to the law presented here as Solicitor General -- will be absent in the decision.  That could lead to a 4-4 split, which then defaults back to the circuit court decisions, all of which have at least partially defended Arizona's argument.