"All displacement vectors are bound ones. They are bound to those points whose displacement they represent. Free vectors are usually those representing global physical parameters, e. g. vector of angular velocity ω for Earth rotation about its axis." "Let v be the value of function $$\vec{v} = \vec{v} (t, P)$$ at the point A in a river. Then vector v is a bound vector. It represents the velocity of the water jet at the point A. Hence, it is bound to point A. Certainly, one can translate it to the point B on the bank of the river (see Fig. 3). But there it loses its original purpose, which is to mark the water velocity at the point A.
"A vector-valued function with point argument is called vector field. If it has an additional argument t, it is called a time-dependent vector field."