The things you need to know from Iron Fist:
-Danny Rand is young, developmentally. He disappeared when he was 10, and has spent the rest of his life isolated from greater society. Maintains that 10-year-old impulsiveness and optimism (people are good, telling the truth is always the best way, etc). This is what gets him into the most trouble in the series.
-The Hand is made up of different sects, which sometimes war against each other in their beliefs of how best to achieve different goals.
-Madame Gao leads one of these sects.
-Colleen Wing used to recruit for The Hand, but then left them (with much fighting).
-Claire is learning to fight because she keeps winding up in situations against thugs and ninjae.