Mixing vectors like recipes
A linear combination is a recipe: take some vectors, decide how much of each (those amounts are scalars), scale them accordingly, and add the results. Think of two paint colors and how much of each you pour in.
v = (1, 0) w = (0, 1) 3*v + 2*w = (3, 0) + (0, 2) = (3, 2)
Span: everywhere you can reach
Now allow any amounts at all. The collection of every point you could possibly hit is the span of your vectors. With v = (1, 0) and w = (0, 1) above, by choosing different amounts you can reach every point on the flat plane — their span is the whole 2D plane.
But a single vector spans only a line — scaling one arrow up and down just slides you along its direction. Two arrows pointing different ways open up a whole plane. The span is simply the answer to 'what's reachable?'
A first taste of redundancy
What if you add a third vector that already lies on a line you could reach, like (2, 0)? It adds nothing new — every point it helps you reach was already reachable. That extra arrow is redundant, and spotting such redundancy is a big theme coming soon.
Here's a lovely fact to keep in your pocket: the span of any set of vectors, taken through the origin, always forms a flat, well-behaved piece of space called a subspace — never a curved or broken shape.