Newton's First Law
When acted on by zero net force, a body at rest or at constant velocity will remain at rest or that constant velocity with zero acceleration.
Equilibrium$$\sum{\vec{\textbf{F}}}=0$$ $$\sum{F_x}=0$$ $$\sum{F_y}=0$$
What does this ultimately mean? When all the forces in all directions are added together and sum to zero, the body is undergoing zero acceleration and will maintain its current velocity or remain at rest.
The above figure has a net force that sums to zero. This means that in this tug of war battle, there is no winner. There is not enough force for player 1 to move the rope to the left or for player 2 to move the rope to the right. The body is in equilibrium!
