Incomplete / Partial responses indicates all responses that started, but weren't completed. A response started when the participant clicked "Next" button in the survey, but did not click the "Submit" button in the end.
Technically speaking, an incomplete response is when there is no SubmitDate in the response table for a response, but the survey was at least started (that is, there is a response row with 1 or more questions answered, but Submit was not clicked, and thus the survey was not completed by the participant.
Total responses is the sum of Full responses and Incomplete responses.
When viewing the Statistics page, the following also applies:
A question with "no answer" counts: when the question was displayed, but the participant hasn't given an answer.
Technically speaking, this is when the question is not mandatory, was displayed, received no answer and the user clicked Next or Submit: the consequence is that the database field for this answer is set to "" (empty string). This "no answer" status cannot be computed for Date or pure Numerical questions where the database field cannot record a string.
A question with "not completed/not displayed" counts: when the page containing the question was not displayed. This can be because of conditions, or just because the participant left the survey before this page was displayed (or just while this page is displayed, but without clicking the Next button).
Also, there is an option on the Response summary page called View saved but not submitted responses: if a participant has started responding to your survey, and then chooses to use the "Resume Later" button to save their progress (which means they haven't clicked Submit to finalize their response), you will see those participants and their responses listed here.