GPS, or to be more accurate, GNSS is a commonly used navigational aid in aviation, especially in smaller passenger planes. Larger airliners are more likely to be also equipped with inertial navigation systems which do not rely on external sources for guidance but they need to be calibrated from time to time to maintain accuracy.
The reason for the use of GNSS systems is its good accuracy and extremely high temporal and spatial availability (system can be used pretty much any time, anywhere) in comparison to the land-based navigation systems.
Loss of GNSS or inertial navigation capability is not safety-critical in the sense that other more traditional navaids such as VOR and radar navigation usually remain available, and in the case that even those fail or are out of reach, there still is the archaic method of using the compass and map, a skill that is required from professional pilots even today.
While I'm not fully briefed in the case in question, it is obvious that the situation was problematic, because due to the problems with GPS signal, the aircraft was unable to execute RNAV procedures in the vicinity of the airfield.
As for the safety implications of this, while it may seem a huge risk, aviation procedures take into account the possible vulnerabilities of GNSS. The devices are redundant and monitor their own performance and the reliability of the signal. Should they detect any anomalies, pilots are made aware of this, and they can use other means of navigation. Pilots also monitor the information provided to them by instruments, and cross-check this with other source to verify reliability.
As the airfield in question (EFSA) apparently did not have air traffic control services provided, there was no other means available to continue safely. It is my understanding that the flight in question was not yet in approach phase. According to AIP Finland EFSA does also provide the more traditional ILS approach which does not rely on GNSS, but as there was no method to reach the initial approach fix with great enough accuracy, the flight had to turn back.
To reiterate the safety of landing using satellite navigation: even if the flight in question was already making an RNAV approach, this method is highly redundant, and unreliable/hacked signal would with almost full certainty lead to a missed approach, and return to point of departure or an alternate airfield.