It would be better to say that acceleration is related to net force. The larger the net force, the larger the acceleration.
This is one part of Newton's 2nd Law. To understand this relationship you must first realize that an object will accelerate only if there is an unbalanced force (a net force) acting on the object.
If all forces are balanced, the object's state of motion does not change (it will remain at rest, or move at constant velocity)
If there is an unbalanced force acting on the object, the object's acceleration will be proportional to the magnitude of this force.
If the net force is doubled, acceleration will double (provided mass remains constant)