Unit content
Span
A set of vectors can generate many other vectors through linear combinations. The collection of everything they can generate is their span:
$$\operatorname{span}(\mathbf v_1,\ldots,\mathbf v_k)
\left{c_1\mathbf v_1+\cdots+c_k\mathbf v_k\right}.$$
Geometric meaning
A single nonzero vector in $\mathbb R^2$ spans the line through the origin pointing in that direction.
Two nonparallel vectors in $\mathbb R^2$ span the whole plane because every vector in the plane can be written as a combination of them.
In $\mathbb R^3$, two nonparallel vectors generally span a plane through the origin.
Redundant generators
Adding another vector does not necessarily enlarge the span. If
$$\mathbf v_3=2\mathbf v_1-\mathbf v_2,$$
then $\mathbf v_3$ is already built from $\mathbf v_1$ and $\mathbf v_2$, so
$$\operatorname{span}(\mathbf v_1,\mathbf v_2,\mathbf v_3)
\operatorname{span}(\mathbf v_1,\mathbf v_2).$$
Span answers a reachability question: which vectors can be constructed from the vectors we already have?