A Jesus Aura is the imaginary light that Christians think emanates around a TRUE CHRISTIAN™. Typically Christians think that non-believers can perceive this light and express it in ways such as "I don't know, there's just something different about you that I don't understand."
(A non-Christian character in the Christian movie God's Club actually says something like this to a TRUE CHRISTIAN™ character, if you want to see how Christians depict this concept in the media they themselves create and consume.)
It may well be that the Jesus Aura comes from popular and classical artwork depicting Jesus and other saints as having discernible golden or white auras of light all around them. This kind of aura is hardly unique to Christianity; most religions use similar imagery in discussing exemplary members of their faith systems and in particular the founders and "saints" in their mythology.
The idea that auras are not only real things but discernible and manipulable ones form the backbone of various branches of woo-medicine as well, despite never once having been demonstrated through reputable experimentation. (The grandest of these debunks happened thanks to Emily Rosa, who is literally the youngest published peer-reviewed scientists in the Journal of American Medicine (JAMA). As a story, it beats God's Club all hollow--and it really happened, unlike anything in that crappy movie.)
Christians try to create this much-desired Jesus Aura through the use of sanctimonious behavior (especially through the use of Jesus Smiles and Preacher Eyebrows), adherence to conservative dress codes, and the presentation of a squeaky-clean reputation, and ultra-ponderous, pithy, artificially deep speech. The idea is to differentiate themselves in every way possible from non-believers, who are imagined to be bereft of hope, divine light, and genuine love, so that those non-believers will suddenly notice in these Christians what has been notably absent from their own lives.
Such Christians think that non-believers will draw closer to the TRUE CHRISTIAN™ who possesses a good blinding-white Jesus Aura--and eventually become more receptive to evangelism through it. (This concept undergirds their understanding of Matthew 5:15 and its imitations in the Gospels: "Neither do men light a candle, and put it under a bushel, but on a candlestick; and it giveth light unto all that are in the house.")
But they also think that people are repelled by it and persecute TRUE CHRISTIANS™ because of how this aura makes them feel guilty about not being Christian. They also refer to the Jesus Aura in describing why a TRUE CHRISTIAN™ should not cultivate close relationships with non-Christians.