Part of macOS
mds_storesSpotlight store
○ Leave it
Keeps Spotlight’s search index on disk.
What it is
Writes and reads the index that makes Spotlight search fast.
Why it might be busy
While Spotlight is indexing. Usually 10 to 30 minutes, longer after an update.
If you stop it
macOS starts it again straight away. Leave it.
The verdict
○ Leave it. Part of macOS, or something that starts again by itself. You never need to close these.
In Activity Monitor
mds_stores
From Procession’s guide, in the words the app shows.