Add a custom object to the 'Related To' lookup for an Event or Task

To enable 'Allow Activities' in Custom Object Definitions

1. Go to Setup | Create | Objects
2. Click Edit to modify an existing custom object
3. Select the Allow Activities checkbox under 'Optional Features'
4. Click OK on the confirmation dialog to finalize

Lightning: 

1. Go to Setup | Object Manager 
2. Open the custom object from the list
3. On the Details click Edit
4. Select the Allow Activities checkbox under 'Optional Features'
5. Click OK on the confirmation dialog to finalize
6. Save

Notes:

• This means that all page layouts created for the custom object will need to be edited and have the related list added.
• To learn more, please review Customizing Related Lists.
• See also Notes on Enabling Activities for Custom Objects