Its when the Linux filesystem detects some inconsistancies and wants to run a full scan to ensure the file system has no errors and to maintain integrity, it will repair any inconsistancies it finds.
Often if a server reboots without a correct shut down then when it boots back up it will run an FSCK. Also if a server has been online for more than 100 days without a reboot, it will run one on its next reboot. Finally an FSCK can be required when the server crashes due to any filesystem error which could be a result of data integrity issues.
You can read more here, where it describes it a lot better than I do:
fsck - Wikipedia, the free encyclopedia