We just heard from NFLPA executive director DeMaurice Smith in a statement issued on Monday. He called the ruling a win for the players and the fans, which is certainly the case from the union's perspective.
If the NFL had been able to identify itself as a single entity then, in theory, they essentially have free reign to control player salaries, free agency and things of that nature. The NFLPA of course doesn't want the NFL to control salaries and really the entire system because that would presumably mean less money in their pockets.
Meanwhile, some also feel that Monday's ruling could have an affect on the overall state of the labor negotiations between the league and the union. Via Yahoo's Shutdown Corner:
[ESPN's John] Clayton intimated that if the NFL lost the appeal, circumstances would lean toward a resolution in the tension that currently affects the 2011 season. "Because, if the NFL wins it, they can really go for the jugular. They can control salaries, and control the system more," Clayton said of a prospective NFL win. "If they lose the case, there may be more of a effort to try and get a [new CBA] deal done."
And a "renewed effort" at getting a labor deal done is what the NFLPA is seeking, according to their statement.