You can assign specific records to users within your account. When a record is assigned to someone, only that user, users with either the manager or owner role, or any custom roles that can "assign records" will be able to view or edit that record.
More details on record assignment, importing assigned records, and how to disable record assignment in an app can be found on the record assignment help article.
Within the record's metadata section is the assigned field where you can view who the record is currently assigned to. If you are a standard user or a user with a custom role that does not have the ability to "assign records" then this will always be your name. Otherwise the role that you have has the ability to assign records, granting you access to records assigned to others.
Notes
Assigning records is intended to be done through the web app or the importer. The mobile apps do not have the ability to assign a record to another user account. They will only be able to assign the record to the user account that created the record if auto-assign records is enabled.
Data events to not currently have any ability to assign records or change what user account the record is assigned to.