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The span of a single vector $\vect{v}$ is the set of all linear combinations of that vector. Thus, $\spn{\vect{v}} = \setparts{\alpha\vect{v}}{\alpha\in\mathbb{R}}$. This is the line through the origin and containing the (geometric) vector $\vect{v}$. Thus, if $\vect{v} = \colvector{v_1\\v_2\\v_3}$, then the span of $\vect{v}$ is the line through $(0,0,0)$ and $(v_1, v_2, v_3)$.
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If the two vectors point in the same direction, then their span is the line through them. Recall that while two points determine a line, three points determine a plane. Two vectors will span a plane if they point in different directions, meaning that $\vect{u}$ does not lie on the line through $\vect{v}$ and vice-versa. The plane spanned by $\vect{u} = \colvector{u_1\\u_1\\u_1}$
and $\vect{v} = \colvector{v_1\\v_2\\v_3}$ is determined by the origin and the points $(u_1, u_2, u_3)$ and $(v_1, v_2, v_3)$.
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If all three vectors lie on the same line, then the span is that line. If one is a linear combination of the other two, but they are not all on the same line, then they will lie in a plane. Otherwise, the span of the set of three vectors will be all of 3-space.