The Custom Field Editor allows you to add your own custom fields to various entities such as Deal Registrations, Leads, Partners, MDF Requests, etc. When you create a new custom field, you have the option of customizing the "API Field Name" (see image), but what is the API Field Name used for?
The Channeltivity Data API allows you to programmatically access entities and their fields. Any custom fields you create are also available via the API. The "API Field Name" field allows you to specify under what name your custom field will be accessible in the API and cannot contain special characters or spaces. If you're not planning on using the API, you can safely ignore the "Customize API field name" checkbox as it won't affect your use of Channeltivity.