The Planck length has no physical significance. It's just a unit of length, chosen for convenience as part of the system of Planck units.

The Planck scale is the scale of lengths/times/etc that are around 1 in Planck units. This happens to be the scale roughly around which the quantum effects of gravity become significant. Since we do not have an accepted quantum theory of gravity, it's therefore the scale at which we cease to have an accepted physical theory.

There is no evidence to suggest that space is discrete at that scale. It's just the scale at which we have no accepted theory, and AFAIK no evidence to evaluate such a theory.