Net force (also known as resultant force) is the overall force acting on an object.
Using the box example you suggested:
if someone was to pull a box across a carpeted floor, there would be a resultant force in the direction that the object accelerates.
Say there is a 100N driving force from whoever is pulling it, the box then experiences 70N drag (50N from friction, 20N from air resistance). The resultant force would be 30N in the direction of the driving force. This is because it is greater than all the forces acting against it combined.
When calculating the resultant forces, assign one direction as the positive direction, and the other as negative (it is often wise to assign the smaller side with negative).
100N - 20N -50N = 30N(+)
and it's positive, so it is in the positive direction (right). If it was negative, it would be to the left.
I hope this helps, and sorry for the childish diagram - it was all my little computer could manage, and I was too picky to use a Google image!. Let me know if I can help with anything else, or if there's an issue with my answer:)