The API Name for a Field is the technical name that is used within a System's API to identify that Field. An API Name can be referred to by other terms such as Internal Value, Internal ID or Item Name in the case of other Systems. The API Name for Fields are all lowercase and will not have any spaces between them. An example of this can be seen below.
In this example you have a Field with the label “Lead Source Detail” serving as the name for the Field (what you see in the application). The API Name for this field is listed as the "internal name" and uses all lower-case text with underscores in place of spacing.
Sync also provides a view into the API Name for each Field within your Field Mappings. The API Name can be found in the Path under the Field Name for any of your mappable Fields.