The precise issue in Canning was whether the president could make a "recess appointment" to the NLRB even though the Senate was holding "pro forma" sessions every three days. Here we delve into oracular text: the "recess appointments" clause of Article II § 2 cl. 3 says that "[t]he President shall have power to fill up all vacancies that may happen during the recess of the Senate, by granting commissions which shall expire at the end of their next Session." The idea is simple: For significant government appointments, the Constitution requires Senate confirmation; but the Senate isn't always meeting, and in a pinch the executive needs to be able to fill a vacancy and ask for approval later.
The details, however, are profoundly difficult, and have been debated since the Washington Adminstration. What is "the recess of the Senate"? Does it mean whenever the Senate goes home for a few days, or only during the breaks between formal sessions? Second, when an office opens up while the Senate is in session, but the Senate goes into "recess" without confirming a successor, does that vacancy "happen" during the recess?
The Republican minority in the Senate hates the NLRB, whose job it is to make sure workers get a fair chance to bargain with their employers. So from 2010 to early 2012, the Republican minority simply filibustered all nominations to the board, with the result that the NLRB fell below its required quorum of three members. In late 2011, Republicans feared that Obama would make recess appointments when they went home for Christmas. They didn't control the Senate, and so to prevent the leadership from "recessing," they used their control of the House to engage in a constitutional trick. Under Article I § 5 cl. 3, "Neither House, during the session of Congress, shall, without the consent of the other, adjourn for more than three days ...." The House leadership refused to consent to a Senate adjournment, so every three days, one member who lived nearby showed up, convened the body with all the élan of Ben Stein in Ferris Bueller's Day Off, and then immediately adjourned. Senate Majority Leader Harry Reid was unhappy -- but the "pro forma sessions" trick was, in fact, one he himself had created during the George W. Bush Administration, as a way of blocking Bush's use of the recess power.
In January 2012, Obama, with the advice of his Office of Legal Counsel, concluded that "pro forma" sessions were not real sessions, and thus that the Senate was in recess. He appointed three members to the NLRB, which began doing business.
One matter that came before it was a complaint against a soft-drink bottling company in Yakima, Washington, that had allegedly reneged on a written agreement with its union. The union won an order against the company in front of the NLRB itself; the company appealed to the D.C. Circuit, however, arguing that the NLRB didn't really exist because three of its members had been "recess appointments."