The number of responses is the number of unique responses submitted for the alert. Depending on how the alert is configured it may be possible for a constituent to submit more than one response. 

The number of deliveries are those responses that were delivered to a target. If a respondent does not live within the district of at least one of the targets their response will not be sent, or delivered. Respondents who do not have an available target for the alert is one possible reason you may have more responses than deliveries.