Normal numbers (scalars) has just a magnitude (the value).
A vector has both magnitude and a direction.
There is several possible ways to represent a vector, but in computer graphics, we often use euclidian space, and there we represent the vector as three scalar "coordinates", x,y and z. (in some cases polar coordinates might be more convenient, maybe using them would have solved the problems the developers had)
Vectors, representing a magnitude and a direction is very convenient when working with positions and directions in space.
A "position" is a vector from origo to the point in space where we want to be.
A "direction" is usually represented as a normalized vector. A normalized vector is a vector where magnitude is always 1.
"up", "forward", "left/right" is normalized direction vectors used to rotate an object in the space.
you need to know these three to know how to place the object in the world.
To get more information on how to do math with vectors, look up Linear Algebra