A Synology drive carries three partitions. The first is the system partition, a few gigabytes, holding DSM and its settings, mirrored by mdadm across every drive in the unit as the array md0. The second is swap, md1, likewise mirrored. The third is the data partition, which joins the other drives' data partitions in the arrays that make up your storage pool. System partition failed is a message about md0 alone: one drive's copy is marked out of date, because the drive was unavailable when the others were written, or because a read of that copy failed.
On its own, on a healthy drive, it is nothing. Storage Manager offers to repair the system partition, which resyncs the small mirror from a good copy, and the message goes away. The concern is what it can be a sign of. A drive that has started to throw read errors will often show them first in the system partition, because DSM reads it constantly, and a system partition failure on a drive whose health status is anything but Healthy is a drive announcing itself. On a pool that is also degraded, it usually means the second failure is on its way.
The trap is the reinstall. Faced with a unit that will not boot cleanly, or a system partition that will not repair, the forum advice is to reinstall DSM, which Synology Assistant offers as Recoverable. On a healthy set the reinstall rewrites the system partition and leaves the data alone. On a set with a weak drive, the reinstall's own writes and the repair that follows can take the data partitions with it, and on an encrypted volume the key vault lives on the partition being rewritten. Image first, and the reinstall becomes unnecessary.