For Jack Wilshere, his career can no longer be defined by potential. At a certain point, that potential has to be turned into consistent performances. The defining moment of Wilshere's career, his performance against Barcelona in 2011, was three years ago. His second excellent performance, for England against Brazil, was nearly eighteen months ago. In between, there have been too many injuries and too many inconsistent performances. There have been flashes of Wilshere's brilliance, but there have also been legitimate questions about Wilshere's development, or lack thereof. Paul Scholes was possibly a little harsh in his assessment of Wilshere, but he hasn't developed much in the past three years, especially on the tactical side of the game, where he seems to have regressed, taking on the worst selfish need to play the hero qualities of Steven Gerrard, his captain at international level.
The World Cup is an excellent opportunity for Wilshere to break out of the bracket labeled "potential" to one labeled "producing, now". Wilshere likely won't start England's first game--Jordan Henderson, Steven Gerrard and Wayne Rooney figure to take the three midfield positions--but Wilshere can have a role off the bench, and in England's other group games, against Uruguay and Costa Rica. The attraction for Roy Hodgson to play Wilshere is clear: there is no player in the England side better at playing under pressure, and Wilshere offers a unique ability to dribble and drive, as well as be creative.
Wilshere having a good World Cup for England would be extremely beneficial for Arsenal. First of all, it would show that he would be fit enough to handle a high amount of games in a short amount of time, something that he hasn't been able to show since he started having ankle issues. Secondly, it would force Wilshere to play in a way that he doesn't at Arsenal. If Wilshere starts for England, he will do so either alongside Steven Gerrard (or were Gerrard to get injured, Jordan Henderson) or at the number 10 role, behind Daniel Sturridge or Wayne Rooney. If Wilshere plays alongside Gerrard, he will have to match the defensive nous and discipline of Jordan Henderson, otherwise Roy Hodgson, who's first concern when setting a team up is its' shape, will not start him.
Thus far for Arsenal, Wilshere has been too indisciplined to play alongside Mikel Arteta and provide the defensive assistance that the more disciplined and more energetic Aaron Ramsey gives. Too often Wilshere bursts forward, then lacks the ability or will to get back and defend, unlike Aaron Ramsey, and unlike Henderson. With Gerrard less mobile than he used to be, England will need the second central midfielder to help shield him; Wilshere won't start in central midfield unless he does that. If he does show more discipline and nous, it makes him a more viable option in central midfield for Arsenal, rather than the wide position that is probably best for him to occupy next season.
The other starting option for Wilshere is in the #10 role. Wayne Rooney currently occupies the role for England, followed by Ross Barkley, much as Mesut Özil plays the role for Arsenal and is deputised by Santi Cazorla and Tomas Rosicky. In both cases, there'd have to be a severe loss of form or injury for Wilshere to be pressed into the #10 role, not least because he has rarely looked comfortable playing there. As Arsene Wenger explained, Wilshere prefers to see the game in front of him, and struggles when he has to play with his back to goal, as someone like Mesut Özil so often does. That also has to do with Wilshere's style--quick, dynamic bursts and one-twos, which he so often initiates, and thus needs to be running forward, so he can accelerate. It's unlikely that Wilshere will, all of a sudden, develop the attributes needed to become comfortable at #10, but it's something that could at least begin to become realistic at this World Cup.
Most importantly, though, is that Wilshere remains fit. Part of the reason why Scholes' argument has credence is that Wilshere hasn't played enough football because injury, and when he has played, he's tried to make up for lost time and has overcomplicated things, rather than remembering that he's part of a team, and doesn't have to do everything himself. The way Aaron Ramsey got back into form was remembering the simple things that he had the confidence to pull off, and then build from there; hence Ramsey had several months of good form before adding goal-scoring. Wilshere needs to do similarly, and that needs to start at this World Cup.