Changing length of spring

In this formula "Fs = kx" what is the force that influences on the length of the spring?

It’s called a restoring force which is any force such that it works to return an object back to its equilibrium position (there should be a negative sign in on the left ie.,

$$vec F = - k vec x$$

to signify that the force operates in a direction opposite to the displacement $vec x$).

For example I figured out if we pull up a mass attached to a spring with a force , the force of gravity will not be effective.

It depends. If the spring is lying horizontally (for example on a level table), then gravity will not stretch the spring. But if the spring/mass system is vertical, then gravity will do work stretching the spring toward the ground.