A dwarf is not commonly seen as a arcane or psionic character. How can I explain in my backstory that my dwarf is able to use psionic powers?
Dwarves aren't commonly seen with psionic powers? Says who? If this is something unique to your setting, you'll have to come up with a story that fits the setting. Otherwise there's no inherent stigma about Dwarves and psionic power use. The psionic power source comes from the far realm and is shaped within one's self: Dwarves are certainly known for their strong self-will.
It's worth noting here that the lore of D&D 4e attributes classes to races by stat, rather than power sources to race by lore. Dwarves are going to be considered commonly anything based primarily on strength, constitution, and wisdom. So they're not going to be commonly thought of as Ardents (cha), Monks (dex), or Psions (int), but Battleminds (con) are totally up their alley.
Evidence of Dwarven Battleminds
- The first big give-away is where Battleminds are first introduced. Page 42 of the Player's Handbook 3, right under the "Battlemind" heading, is the quintessential poster picture of a Battlemind: a dwarf.
- Under Battlemind Overview on the following page, in the section on Race, the very first word is dwarf: "Dwarves and Wilden make excellent resilient Battleminds."
- Psionic Power page 52, the Battlemind Paragon Path Talaric Ironjack, features a dwarf.
- Psionic Power p.122 has a Dwarf Racial Background: Iron Mind
number 4, in particular, might be exactly what you're looking for from an game-lore perspective.
Sources for Dwarven Inspiration
Psionic Power page 40 has a little inset called "Psionics? What psionics?" that describes role-playing a character that is unaware of the source of their power, at least at the introductory levels.
The Dark Sun source material makes the psionic power source very common, and dwarves are certainly not exempt. Perhaps you can garner some ideas from their portrayal and adapt them to your setting.
D&D is a very flexible and open world. Come up with anything you want. I role-played a Minotaur Battlemind who came to her power after being a captive thrall of an Illithid doing experiments on the brains of his victims.
If Dwarven Battleminds are rare in your campaign world, come up with some extraordinary story behind your dwarf obtaining his powers. If nothing else, a rich and vivid back story full of unusual and creative ideas could provide fodder for adventuring later on in the campaign.
There is no canon "This is how Dwarves are Psionic and it is the only way" in all of 4E.
So you could steal this instead:
The Dwarves believe that after you die, you join the Eternal March, where each dwarf walks forever surrounded by his clan. In the front rank walk the Clan Founders and behind each, a banner carrier who leads their particular clan into the unknown. The better you have served your clan, the closer to the founder you will walk. If you shame your clan, you can shave off your hair and beard as penance (or have it done for you if you don’t do it voluntarily). Once your hair grows long again, you are welcomed back into the clan. Those who die with short beards will march in the back but they will still march – this is the Eternal March of the Clans, and all the Clan is welcome.
The Path of Jørn is a new, deviant religion that has its roots deep under the mountains. Jørn was a dwarven miner who was in a collapsed mine and had a bit too long to think about the meaning of life while deep underground. The Path is decidedly non-pacifist, encouraging constant vigilance and physical training in the service of a higher ideal. Jørn never told his first disciples what that higher ideal should be – his philosophy was foremost one of personal improvement. Jørn divorced himself of Clan trappings and dedicated himself to unifying the clans as One Clan of Dwarves, which didn’t go over well with any of the Clan Elders and caused several years of civil war. The current whereabouts of Jørn are unknown – most of his inner circle has been slain and none of the survivors can adequately describe neither his appearance nor his Clan. As a result, the followers who survived the post-war decimation are fragmenting into splinter-sects as this follower or that decides that HIS memory of Jørn is the correct one.
And, of course, the dedication of the Path of Jørn (Plus hanging out in the Underdark with Mind Flayers and other Far Realm beasties) giveth psychic powers. The end.