Positions represent 3 coordinates in 3D space. So, your player's position has 3 coordinates: x,y,z.
A vector can be interpreted as "arrow" from the origin (x=0, y=0, z=0) to a specific point/position in space. Additionally, a vector can be interpreted as well as direction from the origin to this point.
You can add and subtract vectors by adding/subtracting their components. You can even rotate and scale vectors. Just imagine them as arrows and try to add, scale and rotate them. Subtraction is a bit trickier, though: if you subtract one position/vector A form another B (B-A), the result vector returns the direction from point A to B. So, if you would add to the result vector the A vector, your would get the vector which represents the position B.
To determine the distance between two points, you take both vectors of these points, subtract them (so that you get the direction) and calculates the LENGTH of the vector. Just imagine an arrow from A to B.. the length of the arrow is the distance between A and B. In Lite-C you can use vec_length for a given vector to determine his length. But you can also use the function vec_dist to determine the distance between two points/vectors.
So, assume you want to check if you come close to your opponent, which is the you pointer now:
Code:
if (vec_dist(my.x, you.x) < 50) {
//do something
}
There are a lot of tutorial on vector math and what vectors are on the internet, just google them!
i understand it now 
