By default Opportunities in the system are visible based upon your security configuration. You do, however, have the ability to make Opportunities visible to the users whose Contacts and/or Companies are related to it.

This is so that if a Company is reassigned to a new user they can see the Opportunity history linked to their new Company.

If your clients are Contacts rather than Companies, you will want to enable Assigned To users of Contacts with linked Opportunities to be able to see the Opportunities.

To enable this feature go to Settings > Additional Settings > Opportunity Settings:

When this is turned on the Opportunity is visible to the Opportunity record assigned user, the linked Company assigned user (if a Company is linked) and the linked Contact assigned user.