The two, standard Salesforce Objects used in HandsOn Connect are:

Accounts (which in HandOn Connect and for users of Non Profit Success Pack) is generally renamed to Organizations

Contacts

The HandsOn Connect package has dozens of Custom Objects that track data related to volunteer management and the HOC application.  A few of the most important ones are:

• Volunteer Events
• Volunteer Opportunities
• Occurrences
• Recurrences
• Connections
• Volunteer Teams
• Volunteer Team Members
• Locations

There are plenty of others -- some which handle administrative chores - and others which are used for advanced features in HandsOn Connect

Click on the Cog to access the setup menu, then click on Object Manager:

You'll then see a list of all the objects that are available in Salesforce and the HandsOn Connect Application, listed by Label and API name.  You can use the quick find field in the upper right to quickly find an object by name.

Click on the name of the object to access the object details:   (In this example, let's look at the Connection object:

The left menu in an object gives you access to all the components of the object:

• Fields and Relationships -- (a list of all standard and custom fields in the object.  Go here if you want to add new fields or update existing picklist values, etc.)
• Page Layouts -- go here to edit page layouts, create new ones, and manage assignment of page layouts to profiles.
• Lightning Record Pages -- edit or create a lightning record page layout (all the components around and including the Page Layout)
• Buttons, Links, and Actions
• Compact Layouts
• Field Sets
• and all the other characteristics related to that object....

Look for resources in Trailhead to learn more about the structure of objects.

A good place to start is in the module on Data Modeling.