Since this has gone 7 hours, I'll give it an answer, but I welcome any additional answers.
What kind of power is this and why does Gao never use it again
throughout the series?
She prefers not to fight. She'd rather negotiate. I can't explain that exactly or back it up with quotes, but it's rather obvious. She let herself be taken prisoner twice rather than try to fight her way out of those situations.
Why does she let herself be taken prisoner? In part, cause she knows her words can do harm and drive people apart. Her words were very upsetting to both Claire and Colleen.
In part, perhaps, cause she knew Colleen Wing was poisoned and she wanted to wait for an opportunity to arise when Colleen started dying. Something she may have felt, only she could help (not anticipating who Colleen's teacher was)
In part (a personal theory) because she's very patient.
It's worth adding that when she struck both Daredevil and Iron First, neither was expecting it. The outcome might be different if their defenses were up and they knew what she was capable of.
As for what kind of strike, while it wasn't said, it appeared to have some kind of chi to the strike or (possibly) magic.
Madame Gao is clearly someone mysterious. Not only is she able to stun Daredevil and Iron Fist with a palm strike, while looking like a harmless old woman, but the Kingpin respects her and appears, at times, afraid of her. He says "She knows when I'm lying" and when they have a conversation, after Westley had been translating to Mandarin for her at all their meetings, she reveals that she speaks "all languages" and she was able to find the Kingpin's home, something he kept secret. Her line "I'm from someplace further than China" is the clue that's most often referred to that there's something un-earthly in her origin.
Iron First trained in from K'un-Lun, one of the seven capital cities of Heaven. It's often speculated that Madam Gao is the Crane Mother, the ruler of the K'un-Zi. Now, the Crane Mother's the ruler and not the champion. Theoretically, the champion would be more eager to fight.
K'un-Zi is (in the article above), is a "City of dark magic". So it's possible that her power is dark magic, not chi. How that would reveal as different in future writing isn't clear. Marvel is kind of tiptoeing around the whole "Magic" thing, Spells are just programs, etc.
There are inconsistencies between the comics and the Netflix series. K'un-Lun and the Iron First were never the "enemy of the hand". The Hand was earthly, K'un Lun only had a gateway to Earth every 15 years. There were conflicts between the capital cities, but the Hand wasn't part of that, so they've made some changes with the original story.
In the comics, the Chaste was the enemy of the Hand. Stick, Daredevil's teacher, was the head of the Chaste.
All that said, what works about Madame Gao is her mysteriousness. She's a fun character, from someplace farther than China. Precisely who she is hasn't been revealed and as a result, how she does what she does isn't 100% clear. The Crane Mother is a popular theory though.