Parity is when talent has been diluted to the point that marginal teams can jump up and have "one year wonder" type years and the great teams aren't always GREAT. Talent has thinned out to the point that any team, if they make the right moves can have a shot at being a championship team whereas in a more competitiveness the resources are more scarce and it takes a good GM/front office to spot the right talent.
To put it another way sports in general has become more player oriented rather than front office oriented where the impact is on the front office and coaching staffs to build a competitive team.
Parity also brings down the level of play somewhat. I think we can all agree that players today are bigger and stronger than they were 10-20 years ago but at the same time because the talent pool has been thinned out we're seeing talent that normally wouldn't be starters taking on starting roles. The dilution of talent means the fundamentals have been lost a bit.
This is a problem in all sports and I think that the NFL has seen parity bring down the level of play and made it easier for average teams to have a shot at winning it all but it sure as heck isn't as bad as the NHL and the NBA to a lesser extent where rapid expansion (NHL) and too many underclassmen (NBA) has really brought down the level of play AND made for an artificial competitive balance.
The NFL's expansion while not being extreme has helped to spread the talent pool a bit and the insistence on rushing drafted players to be impact guys has hurt the league and its level of play which has brought some parity to the fore. I still agree with untrugby's point that the NFL is quite competitive because it hasn't been bogged down as much by it the way other leagues have.
(For what it's worth MLB is probably the most bullet proof against parity as it actually takes some shrewd front office work to build a team and the willingness/money to keep a team's nucleus around)