I got the following health status when logging in to vCenter Server Appliance console the other day. Not quite sure how to proceed to fix this. Using the Google machine, there are several scenarios where you could clear out the files or expand the drive size.
Fix Threads:
VCSA 5.5: vCenter 5.5 appliance space issue /storage/core out of space
Different folder: The / filesystem is low on disk space or inodes VCSA
Increasing Drive Size VCSA 6.0: Increasing the disk space for the VMware vCenter Server Appliance in vSphere 6.0 (2126276) | VMware KB
Deleting Files VCSA 6.0U1: How to Fix /storage/core filesystem Out of Disk Space Error on VCSA 6.0U1
This is what I'm seeing in my /storage/core folder:
I'm not sure if it's safe to clear out the folder, or to expand the drive. I'm afraid there's another issue that is causing the folder to fill up, so either of these "fixes" may just be a bandaid to the underlying issue.