A force represents an interaction that can change an object's motion. Forces have both magnitude and direction, so they are vectors.

The SI unit of force is the newton:

$$1,\mathrm N=1,\mathrm{kg,m/s^2}.$$

Forces come from interactions

A force is always associated with an interaction: gravity between masses, contact between surfaces, tension from a rope, electric interaction between charges, and so on.

A force is not something an object simply “contains”. It describes how another object or field interacts with it.

Net force

Several forces can act on the same object at once. Their vector sum is the net force:

$$\mathbf F_{\mathrm{net}}=\sum_i\mathbf F_i.$$

Two equal forces in opposite directions can therefore produce zero net force even though both forces are present.

Components

A force can be resolved into coordinate components just like any other vector:

$$\mathbf F=(F_x,F_y,F_z).$$

This allows several physical interactions to be combined into one vector quantity that can be related to the object's motion.