Describes someone who acts impulsively or is boisterous; can be used for a tomboyish girl or a reckless person of any gender.
She's been a tomboy since she was little, often climbing trees.
That rash person is making another reckless plan.
無鉄砲 is an adjective/noun meaning reckless or foolhardy, focusing on the lack of caution, whereas 跳ね上がり者 emphasizes the person's impulsive, boisterous nature.
Compound of 跳ね上がる (to jump up, to be impetuous) and 者 (person). The exact historical derivation is uncertain, but the word literally suggests a person who 'jumps up' or acts impulsively.