A block with mass $m$ is put on top of a surface. The friction coefficient between block and the surface is $\mu$.
The normal force is $m g$, so the maximum static friction $F_\mu\le m g \mu$.
It means when the external force is less than $m g$, the friction force is $- m g$.
However, if the external is larger than the maximum static friction force then the friction force stay constant $- mg \mu$.
And the block starts to move.
The following simulation let you play with the above case.
You can drag the spring horizontally to change the external force.
CLick the following image to display the simulation.