All your development is done here. From creating reports, charts, formatting them, putting them together as a dashboard all the work is done on Tableau Desktop.
Tableau Desktop is used to visualize and analyze data, create workbooks, visualizations, dashboards and stories.
The dashboards you create are shared with other users using Tableau Server. When you upload(publish) a Dashboard to Tableau Server from Tableau Desktop, other users can access those Dashboards by logging on Tableau Server.
Tableau Server and Tableau Online allow you to safely distribute the interactive workbooks to the right people. You can edit workbooks, visualizations, dashboards and stories in Server or Online, but you can't produce new ones. The editing options are limited compared to the Desktop.
Server and Online can be used as high-performance data repositories for Desktop users.