usually it means that the vector can be written as a linear combination of two other vectors you know beforehand.
one vector determines a line, two vectors determine a plane.
there are two different ways of thinking of a vector: one is simply as a point.
another way, is as an "arrow" going from one point in space, to another. in this view, all "arrows" with the same length and direction are considered "equal".
the bridge between these two views is to identify a point in space with the arrow that goes from the origin, to that point.