It’s an expression from a different age that has mostly retained its meaning while its components “take” and “care” have undergone semantic shift.

The word “take” originates from Middle English “taken,” which comes from late Old English “tacan,” meaning “to grip or seize.”

The word “care” originates from the Old English “caru” or “cearu,” meaning sorrow, anxiety, or grief, specifically the type by which one person has concern and takes responsibility for the situation.

So “take care” could be translated as “seize empathetic responsibility” and is a way of showing the speaker’s wish that the other person behaves in a socially responsible manner.