What is GPS HIL in layman's terms?
The true position of an aircraft in flight can be measured, but the accuracy of any measurement is limited. The actual measured position is the actual true position plus the actual measurement error. Each error of position measurement is 3dimensional. If observed over a long time, the distribution of the errors will have a shape and size that is characteristic for the measurement method.

For GNSS receivers, the measurement of the latitude and longitude measurements depend on each other, while the vertical measurement of altitude does not correlate much with the horizontal measurement. This is why the usual model to describe is a cylinder:


Image source: ESA

The Horizontal Protection Level (HPL) is simply a horizontal cut through the cylinder where the aircraft is located with an acceptable level of probability.
The cross section of a cylinder is a circle, and the radius of this circle is the horizontal performance requirement. 

The HPL is just a geometric definition. It is useless without acceptance levels and performance requirements, which are not part of its definition. Those emerge from the performance of an GNSS augmentation system like WAAS for GPS or EGNOS for Galileo, and the requirements for the use in aviation. Here below is a table of GNSS augmentation performance requirements by FAA for different phases of flight:


Image source: ICAO