I see there is a lot of debate about Wright's value to the team, so here's my two cents.
The "move tight end" or, in other words, the big wide receiver who doesn't block and typically lines up on the inside but can be flexed out (or even occasionally put in the backfield), has become almost a regular position in the NFL. Almost all of the good offenses in the last five years have had someone at this position who makes a big impact.
Patriots- Aaron Hernandez
Saints- Jimmy Graham
Packers- Jermichael Finley
Broncos- Julius Thomas
49ers- Vernon Davis
These guys cause a big problem, as we've seen with Hernandez and Thomas first hand, since they require a defense has a freak Jamie Collins-type or a big defensive back (think Talib on Graham) to shut them down. Of course, it often requires the defense's best player to move to cover the move tight end, leaving someone else to handle the outside receivers.
Particularly with the Patriots history of the two TE offense, I think it's critical that they have someone who is a threat in that position. If Gronkowski is injured, we saw that Hernandez did a good job picking up the slack, even though he was not a blocker, the offense was still breaking records. When Gronkowski is on the field along with the TE2, the offense is running at full strength, and we've seen how unstoppable they can be.
I am guessing that Belichick brought in Brandon LaFell as a guy who could fill-in as the move tight end from time to time, but I think that Wright fits the mold better and provides depth to a position that is overlooked, as some think he is a "backup tight end" when in fact his role in the offense is critical. In addition, there are very few real "move tight ends" in the NFL that can really play the position well, which is why we've seen teams try to convert basketball players like Graham and Thomas. Basically, it is someone who is in between a WR and TE but who can handle the physicality of playing inside. Wright was a WR in college.
I don't think that he is that similar to Hernandez in the sense that he isn't as shifty or fast, so I'm not expecting miracles, but he is far better than LaFell at that position. Just because he doesn't have the talent of Hernandez doesn't mean he won't be very successful in this offense. Hernandez was more explosive, but Wright is 6'4", whereas Hernandez was 6'1". He will be difficult to cover in other ways.
Hernandez and Wright had roughly the same amount of catches, yards, and TDs in their rookie years. Hernandez had Brady, whereas Wright played in one of the worst offenses in the NFL.
Belichick likely got the inside info on Wright through Schiano.
I like this acquisition. I predict he will have a much more important role in the offense that people are forecasting.