The labor contract they are referring to is the collective bargaining agreement that the NFL Players Association and the owners signed a couple of years ago. It states that the players must earn 60% of the total revenue for the league, with the owners getting the other 40%. It also helps establish where the salary cap is set.
The owners opted out of it because they feel they aren't making enough money (their share was an estimated $4 billion last year). The current agreement was suppose to run through the 2013 season, but with the opt out, the agreement will end in 2011. This gives the NFL PA and the owners about 2 years to work out a new agreement.
If a new agreement is not in place by the 2010 season, then that season could be played without a salary cap (which I believe would be the first time since 1994). Also, the owners are going to push to have a rookie pay scale set in place, much like the NBA.
If this agreement is not completed by the 2011 season, then there could be a potential lock-out. However, many experts and NFL insiders agree that it is highly unlikely that this will happen because of the massive revenue loss that by sides would take.