Geometrically, what is the span of vectors? Simple question from a calc 3 beginner. Visually I cannot imagine the span of two vectors, what does this necessarily mean? For example my text mentions if two vectors are parallel their span is a line, otherwise a plane. Can anyone elaborate?

Here is a visual way of thinking about this (at least in small enough dimension that you can visualize it).
Say you have some collection of vectors and you place yourself at the origin. Each vector determines a direction (the span does not care if you replace a vector by some non-zero scalar multiple), and the span is everywhere you are able to go by only going in the specified directions (though you are allowed to go both forwards and backwards).
So, if you were in $3$ dimensions and had the vectors $(1,0,0)$ and $(0,1,0)$ then you could for example go to $(-1,2,0)$ by first going backwards $1$ unit in the direction of the first vector and then going forwards $2$ units in the direction of the second vector.
