Use of the GPS 1PPS feature in a system
PPS is not a fundamental function of GPS receivers. It is a axillary function that a GPS receiver can provide from it's internal timing systems that are used for actually measuring GPS position.

However, in many contexts, having a very precise local timestamp is highly beneficial. It is these applications where the PPS output is helpful.

Take a example where you have two sensor systems, perhaps a mile or two apart. They're going to have separate local clock oscillators, which will have different drift rates. The PPS signal, referenced to the GPS timestamp, is extremely useful for providing a way to accurately determine timing between the two systems. The GPS system compensates for the transmission time between each receiver and the GPS sattelite, so the PPS signals can be said to occur "simultaneously" to a considerable degree of precision, sometimes greater then the actual time-of-light transit between their positions!

For example, the LEA-6T timing GPS has a RMS time-pulse (e.g. PPS) output accuracy of 30 nanoseconds. Critically, that timing accuracy is position invariant compared to a theoretical global GPS time-base. 

Note that this has fun effects like making the effects of the theory of relativity important to measurements. Light travels ~11.8" per nanosecond, but the GPS PPS output has a functionally infinite propagation speed, as all PPS pins theoretically would go high within the error band (~30 nanoseconds), invariant of their physical distance. 

This works because the PPS output is not driven by an external pulse, but rather an internal clock that is adjusted to account for distance from the GPS sattelites, so each GPS receiver independently maintains it's own timebase, and the system conspires to make each discrete timebase phase and frequency align with each other.



Edit: You are asking about inertial measurement and navigation systems? If you're asking for the role of a PPS signal in something like a IMU, there isn't one. It's not used, except perhaps for setting the clock of the IMU's output timestamps (if it has timestamps).

To be clear, GPS systems are a critical component of many IMU systems, but the IMU uses the position output of the GPS, not the precision timing output.