When a test class fails with an "Insufficient privileges" error during deployment, it indicates that the user profile under which the tests are being executed doesn't have the necessary permissions to perform the actions required by the test. In a sandbox, the test might have been running with a different set of permissions compared to the production environment.
By using System.runAs(), you can specify a user context in which the test should run, which allows you to simulate the appropriate permissions. For this to work, you need to create a User instance in your test class with the profile that has the necessary permissions and then enclose the logic of your test within a System.runAs() block with this user.
This is a preferred solution over seeAllData=true, which would give the test access to all data in the production environment, potentially leading to tests that are not isolated and thus less reliable. It's also preferred over changing organization-wide settings or relying on specific setup in test classes, such as making sure Test.startTest() is not inside a loop.
References:
Salesforce Documentation on Using the runAs Method: Testing with the runAs Method Salesforce Help Article on System Permissions: Profiles and Permissions