Walt is "special"
According to Lostpedia:
People have noticed something "special" about Walt throughout his life, and he seems to have psychic powers of some sort.
In his flashback episode, called "Special":
Brian also admitted that he was afraid of Walt, saying: "There's something about him. Sometimes, when he's around, things happen. He's different somehow."
One thing that made Brian suspect Walt was "different" happened shortly before his mother Susan's death. As Brian and Susan were discussing her recently diagnosed illness, Walt was studying a book of Australian native birds, seemingly oblivious to the conversation happening in the room. He wanted Brian to look at the entry for the Australian Bronze cuckoo. When Brian ignored him, Walt became angry and insistent, demanding "You're not looking!" Suddenly a bird slammed into the sliding glass door, killing itself on impact. It was an Australian Bronze Cuckoo.
He's referred to as special at least three times:
Ben refused, saying Jacob wanted him there, and that Walt is important and special.
Later, Juliet commented to Michael that Walt was special, that he wasn't an ordinary boy, and that's why she was worried about him.
As Walt brought up his kidnapping by Ben years ago, Ben apologized and once again referred to Walt as "special."
Tom said that while in their care, Walt was safe, along with Zach and Emma. Tom also said that Walt is "special".
Boring "official" answer
The Triva section answsers:
At Comic-Con 2011, co-creator Damon Lindelof stated that the source of Walt's powers was never meant to be full-throttled mystery. He said the answer to question, "why is Walt special?" is that "because he is" and nothing more.
The cited source, HitFix adds:
(That said, because they had expected to be canceled after the first 13 episodes, they never banked on having to deal with Malcolm David Kelley's growth spurt, and at that point had to write him out, only giving Walt some semblance of closure in the bonus epilogue, "New Man in Charge," on the complete series DVD set.)
Unofficial fan answers
Lostpedia lists as one of the Unanswered Questions:
Why is Walt "special"?
These Unanswered Questions are not to be answered on the main page, and are to be kept open-ended and neutral without suggesting an answer. Instead, many fan theories are offered. There are many; some are:
- Walt is "special" because he can manifest his thoughts into reality.
- In the episode "Special" (Season 1) while playing backgammon with Hurley, Walt thinks a number out loud and then rolls it.
- In the episode "Special" when Locke is teaching Walt how to throw knives, Locke says, "Imagine it in your mind's eye." When he does, Walt is right on target.
- In the episode "Special", When studying native Australian birds, Walt tries to get his distracted stepfather's attention to look at the bronze cuckoo and when he can't a bronze cuckoo flies into the back door and kills itself.
- In the episode "Special", Walt is chased through the jungle by a polar bear after reading a comic book with a polar bear in it.
- All of the above stems from the exposure Walt had to a source of electromagnetic energy in Australia.
- Much of the apparent psychic ability Walt has displayed while on the Island may stem from his reading of the Green Lantern comic book. Inspired by this, Walt may be the so-called "the magic box".
- In "Special", Walt's ability to see with his mind's eye is a sign of the artistic vision he received from his father.
- Walt's powers may be, in essence, a "younger version" of the same abilities that Desmond has.
- Walt is "special" because his body and mind both travel time as opposed to Desmond who has only traveled with his mind.
- Walt can teleport because the MIB could not have been Walt so he had to of been the actual Walt who appeared to Locke and Shannon.
There are lots more theories at About.com's lost pages: Unanswered 'Lost' Question - Why and How was Walt Special?.