I have learned that a scalar is simply a value, a number, as Matt described.
A scalar doesn't really exist at the origin or any other position, because it doesn't have a multi dimensional position at all.
A vector is a way to describe the position of a point in space, and it's direction from the origin.
The way to write a 3D vector is [x;y;z]. For example, the vector [1,2;3] describes a point that it 1 step away from the origin on the x axis, 2 steps from the origin on the y axis, and 3 steps away from the origin on the z axis.
Now, if you multiply [1;2;3] with a scalar (let's say 5), it works like this:
5 * [1;2;3] = [5*1;5*2;5*3] = [5;10;15]
The result defines a new point in space, that has the exact same direction from the origin, but now farther away, at exactly [5;10:15]
Cheers
Frank