Hehe I see... well multiple interested fellows seems a good reason to write a reply
The 'standard' way to describe a (bounding) box, in mohaa, is by means of a 'mins' and a 'maxs' vector. Conceptually, the mins vector points to the lower left corner while the maxs vector points to the upper right corner. All values in mins must be smaller than those in maxs for a positive volume (otherwise your box is 'inside out'). These vectors are defined with respect to a particular coordinate system (for you to choose). Typically you would take the world coordinate system. That was the part on how to store the information.
Now how to determine whether a particular object is inside it... if your bounding box is
axis aligned, which essentially means its sides coincide with (x,y,z) grid lines, this check is relatively easy. A
point (e.g. the
origin of a player) is inside the rectangle if and only if:
mins[0] < point[0] < maxs[0]
mins[1] < point[1] < maxs[1]
mins[2] < point[2] < maxs[2]
Thus you consecutively check for the x, y and z coordinates to be within the bounding box. Only if all these 6 conditions are satisfied, the point is inside the box proper.
If your box is not axis aligned, i.e. rotated in some way with respect to the grid, things get a bit more complicated. In that case you have to transform either the coordinates of the point or those of the box bounds to the rotated coordinate system. It's definitely doable, but I'll skip that part for now as I'm assuming you only need an axis aligned box.
Hope this helps!
Hint: you can find lots of help on this topic if you google for axis-aligned bounding box (AABB) intersection test.