The payback period is how long it takes for your cumulative electricity savings to equal what you paid for the system. After that point, the energy your panels produce is essentially free for the rest of their life.
Payback is shorter when electricity tariffs are high, sunlight is strong, and the system is well-sized. It's longer when you add batteries (they add cost without adding generation) or oversize the system beyond your usage.
Since quality panels carry 25–30 year performance warranties, most systems spend the majority of their life producing free electricity after payback.
This is general guidance — figures vary by location, tariff, equipment and installer. Always confirm details for your own home before deciding.