Short answer
HubSpot's KB: data sync keeps contacts consistent between HubSpot and your personal Outlook contacts folder. Choose one-way to HubSpot, one-way to Outlook, or two-way, with criteria for which contacts are created. The integration has 14 default mappings that can't be edited; you can add new field mappings.
1. In HubSpot
The relevant screen in my demo portal.

2. Worth knowing
Check the KB's limitations list before turning on two-way sync with a large database.
3. Related
Data sync field mappings and calendar sync.