Plain English Meaning
It is the row on a GPS approach chart that tells you how low you can descend when your GPS is giving you very accurate left-right guidance but no up-down guidance. You level off at the listed altitude and look for the runway, just like on a non-precision approach.
Full Definition
The Localizer Performance (LP) lines of minima are the published approach minimums on an RNAV (GPS) instrument approach chart that apply when the aircraft is using WAAS-based lateral guidance with localizer-like precision but without vertical guidance. LP minima provide a () — not a — and are flown as a non-precision approach with tighter lateral than .