Power BI Desktop
If you look in the Microsoft Store you will find two applications that you can install on your Windows PC. One is Power BI Desktop and the other is Power BI Mobile.
Install the Power BI Desktop if you are planning to create reports in your organization. All Power BI products (Service, Desktop and Mobile) are used with the same Power BI Licence you have.
Power BI Desktop is a Desktop application similar with Excel in some ways. It installs on your computer and you can import data, transform data using formulas, merge data, create data models that help you combine multiple data sources into one (similar with a database model). With Power BI desktop you also build your reports, build interactions within your report, create filters. And once all that is done, you use Power BI Desktop to publish the reports to Your Power BI Service that will take it from there.
Imagine Power BI Desktop as your kitchen where you create recipes, experiment and play. While Power BI Service is the cooking blog that you use to share your work.
The last element is the Power BI Mobile. This is just used to display the reports and dashboards created on mobile devices.