You can connect Snyk API & Web with either Jira Cloud or with your own Jira Server instance. This enables you to have two-way synchronization of your findings with Jira, meaning that a finding that is reported by Snyk API & Web is sent to Jira and as soon as it is closed it will trigger a re-test. If the finding is fixed, the Jira issue is kept close, otherwise, it is reopened.
Regardless of your Jira setup, you need to choose which targets to synchronize and how (either manually or automatically). The options available are the same for both Jira Cloud and Jira Server.