It just means that the pendulum will only execute SHM with small angles for which the pendulum subtends as it oscillates.
For larger angles the motion of the pendulum deviates from being simple harmonic; that's why the small angle approximation is required in the derivation.
EDIT:
Even for a horizontal mass-spring system the displacement of the mass from its equilibrium position cannot be made too large, otherwise the simple-harmonic motion ceases to be valid.