The Present (2014 Season)
Barbre's extension doesn't really have a major impact on this upcoming season because he was already under contract for 2014. Barbre will likely assume his role as the team's sixth offensive lineman behind the starting five of left tackle Jason Peters, left guard Evan Mathis, center Jason Kelce, right guard Todd Herremans, and right tackle Lane Johnson. Barbre serves as the backup to every single player save for Kelce at center.
The Eagles offensive line stayed remarkably healthy in 2013. The starters started all 16 games for the first time since Philadelphia's 2006 season. The Eagles probably can't count on that happening again, despite the power of Chip Kelly's sports science program, so Barbre is definitely a valuable player to have right now.
Some may argue that Barbre could unseat Herremans, who admittedly struggled in 2013, but this seems unlikely. Keep in mind the bulk of Herremans' struggles happened at the beginning of the season while he was still adjusting to a position change and spent the offseason rehabbing from a foot injury that ended his 2012 season early. Herremans seemed to play better as the year went on, and he was especially effective as a run blocker in Kelly's rush heavy offense.
The Future (Beyond 2014)
The concern with the future has to do with the reality that the Eagles have the second oldest starting offensive line in the entire NFL. Barbre will turn 31 after the 2014 season (June 22, 2015). He'll still be slightly younger than starting guards Evan Mathis, who will be 34 (Nov. 1, 2015), and Todd Herremans, who will be 33 (Oct. 13, 2015). If Mathis and/or Herremans show major signs of decline in 2014, the Eagles could part ways with them after the season. Cutting Mathis (which seems like blasphemy at this point) in 2015 would save the Eagles $4.5M and incur $2M in dead money. Cutting Herremans (who hasn't played as well as Mathis) in 2015 would save the Eagles $2.8M but also incur $2.4M in dead money.
If Mathis and Herremans both play well enough in 2014, the Eagles could afford to bring back both as starters and have Barbre be the backup yet again for 2015. In 2016, however, Mathis can be cut to save $6M ($1M dead money) and Herremans can be cut to save $5M ($1.2M dead money). At that point Mathis will be going on 35 and Herremans will be close to 34. Barbre will be 33 and could be a stop-gap starter while the Eagles search for more viable long-term answers at the position.
If the Eagles feel comfortable enough with Barbre starting at tackle, they could also use him as a Peters replacement as soon as 2016. Peters, who will be 34 in 2016, can be cut for a savings of $6.3M ($3M dead money). In this scenario Lane Johnson would likely move over to left tackle while Barbre would play over on the right. I don't think this situation is as realistic as the ones that involve Barbre taking over for Mathis or Herremans at guard, but it's worth noting at least.
The Bottom Line
Barbre's deal gives the Eagles flexibility. At the least, it gives them a top quality backup at 4 out of the 5 offensive line positions for the next few seasons. At the most, it gives them a cost-effective replacement who can take over as a starter should the Eagles part ways with one (or more) of the current starters in the future. Either way, it's a win-win for the Eagles.
The only downside here is that Eagles offensive line is still really old (football wise, at least) and lacks any kind of long-term options save for Lane Johnson and Jason Kelce. Barbre may ultimately buy the Eagles some time in looking for replacements, but eventually the team needs to be prepared for the future in order to not have to replace multiple starters all at once.