each one, every single member of a group considered one at a time
Hekastos is the New Testament's word for picking a group apart and pointing at its members one by one. Where another Greek word, pas, sweeps a whole crowd together as "all" or "everyone," hekastos slows down and says "each one," insisting that the group is made of separate individuals who must be counted, addressed, or answered for singly.
This distributive force, the idea of "one apiece" or "every single one on his own," is the same in every place the word appears, which is why it has a single meaning. The flavor only shifts with the context. It can be tender, as when Jesus is said to lay his hands on each one of the sick brought to him. It can be sobering, as when Paul says each of us will give an account of himself to God. And it often pairs with a possessive to drive the point home: each in his own language, each according to his own labor, each carrying his own load.
Because the word so naturally fits matters of personal responsibility and reward, the New Testament leans on it heavily when it speaks of judgment, spiritual gifts, and the duties believers owe one another. The recurring note is that no one is lost in the crowd: God deals with people, and people answer to God, one at a time.