to divide something into parts, especially into two, and so to reach a halfway point
At its core this verb means to split a single whole into parts. Most often the split is into two, which fits its close tie to the noun for "half": Jacob divides his company into two camps, the spoil of war is divided into two shares, and the Jordan parts to one side and the other so people can cross on dry ground. But the parts need not be exactly two, since Gideon and Abimelech each divide their men into three companies, and traders divide a great sea creature among many buyers.
The verb works the same whether someone actively does the dividing or something is described as divided: the waters part, and a kingdom is torn into pieces. That is one action seen from two sides, not two different meanings.
A second, quieter use grows out of the same idea of the halfway mark. To speak of days that are not "halved" is to say a life is cut off before it reaches its midpoint, and a flood that "halves" the neck is one that rises to the middle of it. Here the word is not about splitting an object at all but about arriving at the center point of a span.
Related Hebrew verbs carry neighboring ideas: one word (חָלַק) is about parceling something out as portions to different people, and another (בָּקַע) is about cleaving or bursting something open by force.