Assignment Objects are Asset Type Custom Objects being transferred from an existing Contract record to an Assignment record. The Assignment Object(s) only appear when the existing Contract record has an Asset (Custom Object) to transfer.
For this example, the Contract record has a Walk-in Freezer as an Asset (Custom Object).
On the Assignment record, the corresponding Asset (Custom Object) has an + Add button to transfer the Assignment Object to the record.
To finish adding the Walk-In Freezer, click the Add to Record button and Save the record.