Calibre maintains 3 dates in standard metadata: date, pubdate, and last modified. When you send books or metadata to CC, these dates are passed and stored unchanged. The first two, date and pubdate, are shown in book details as "Added to calibre" and "Pub date" respectively. Both of these dates can be added to the Group menu; see this post for details
. The last modified date is not displayed, but is used to determine if CC's stored metadata needs to be refreshed. Any custom column dates are also passed to CC, stored unchanged, and displayed in book details. CC does not sort on any dates in custom columns, but they can be added to the Group menu.
In addition to the above, CC maintains two non-calibre dates: metadata last modified (called "Updated" in CC) and date last read (called "Last read" in CC). The first is set to "now" whenever calibre sends metadata to CC for the book in question. The second is set to "now" whenever a reader is launched for a book. CC displays and can sort on both these dates.