Nothing specific to geo-caching here. More about GPS and cell-assist.
The thing about most mobile phones is that they have quite wimpy GPS capabilities. This is a function of the power draw and the limited antenna available. In order to make the GPS in a mobile phone function more usefully, phones look around at the nearby cells, and work out a fast approximation to where they are. This knowledge makes the job of the internal GPS receiver much easier. With a very good clue as to where it is, and what the precise time is, a GPS receiver can lock onto the signal from the GPS satellites much much faster. The difference in time makes the difference between a useless GPS capability, and a quite reasonable one. Cell assist also helps in areas with lots of buildings, where there is not much sky visible, and GPS really struggles.
Without any cellular assist a typical mobile phone will still navigate with its GPS, but it will struggle at best. It may take a long time to settle down and achieve a lock. So much so that you could probably forget geo-caching.
A GPS receiver will work anywhere on the planet. They receive signals from satellites in orbit around the Earth, and work out your position from the very precise knowledge of those satellite’s orbits and very very precise timing of those signals. The GPS satellites carry atomic clocks to ensure the needed precision. Famously they are so accurate that they need to take into account general relativity in order to maintain this accuracy. The deep internals of how the satellite signals allow you to work out your position is complex, but at its base, so long as you can see four satellites (and they are in reasonably well separated locations in the sky) there is enough information for the receiver to work out what the time is, and hence how long it took the signals to arrive from the satellites. That allows you to triangulate your position. Modern receivers use as many satellites as they can see, so when there are more than four the precision improves. They also use a lot of very spiffy algorithms to filter and predict what is going on with the signal, and from this they can achieve precision that is as close to pure science fiction as you may like.
A dedicated GPS receiver will have capabilities that make your phone’s GPS look very mediocre. Cell-assist is a cheap way of approximating what a good dedicated receiver is capable of.