I didn't understand what do Bulk and Notification labels mean and how they work. Could you explain me which is their inteded behavior?
These are Gmail smart labels, Gmail automatically categorises emails and assigns them these labels where appropriate.
The definitions of
Bulk mail includes any kind of mass mailing (such as newsletters and promotional email) and gets filtered out of your inbox by default (where you can easily read it later)
Notifications are messages sent to you directly (like account statements and receipts)
Extracted from this Google Blog Post about smart labels