TFS4JIRA Synchronizer is a web application accompanying JIRA plugin.
This component must be installed in order to TFS-JIRA issues synchronization work. However, if you don't need this feature and TFS check-ins synchronization feature is enough for you, you don't have to install it.
TFS4JIRA Synchronizer installation process is quite straightforward. Simply run the installer (tfs4jirasynchronizer-xxx-yyy-zzz.msi) and follow instructions. The installer will warn you if any of the required components is missing (see this page for a list of prerequisites). TFS4JIRA Synchronizer installer requires that at least one IIS site is defined.
You should be able to access the installed application under the following URL: http://<your-iis-host-name>/tfs-jira-synchronizer.
TFS4JIRA Synchronizer application can be installed on any server machine that has network access to both JIRA and TFS and which is always online.