In a short article posted just prior to the oral argument, the SCOTUS blog, the best source of information for Supreme Court news, explained the background of the issue this way:
42 U.S.C. § 1983 provides that any person acting “under color of” state law who deprives another person “of any rights, privileges, or immunities secured by the Constitution and laws, shall be liable to the party injured.” Section 1983 principally serves to regulate the conduct of government employees. But private individuals, too, can be liable when they are clothed with governmental authority.You can read the full article here.
The immunities available under § 1983, however, do not necessarily follow § 1983 liability. Private persons sued under § 1983 may not be entitled to qualified immunity — which is available to a defendant unless he violated “clearly established” legal rights, of which a reasonable person would have known — even when government employees would be immune under identical circumstances. So held the Supreme Court in Richardson v. McKnight and Wyatt v. Cole. Nonetheless, those decisions acknowledged that private individuals might be entitled to immunity under different circumstances.
The case of Filarsky v. Delia forces the Court to explore those circumstances once again.
After the oral argument, the blog posted that the "oral argument in Filarsky v. Delia veered in several directions, even discussing matters well outside the question presented. By the time the dust had settled, though, a majority of the Justices seemed inclined to hold that Mr. Filarsky – a private attorney who had provided services to a city government – was entitled to the protection of qualified immunity. More difficult to discern was the Court’s preferred rationale." The full post oral argument analysis is available here.
Finally, go here for access to all the relevant documents related to the case including the briefs, the lower court's opinion and the transcript of the oral argument.
UPDATE: You can now listen to the oral argument here.