Publish (Home ribbon) sends a .pbix file to a workspace in the Power BI service. It creates two items: a report and a semantic model (the data and measures).
My workspace is personal. Team content belongs in a shared workspace, where people get roles. To distribute to a wide audience without giving them workspace access, publish an app from the workspace; an app can have several audiences that see different content.
In the service you can also build a dashboard: one page of tiles pinned from reports. Dashboards are made in the service, not in Desktop.
To push content to people, set a subscription (a scheduled email with a snapshot of a page). To be told when a number crosses a threshold, set a data alert on a dashboard tile showing a card, KPI or gauge.
Endorsement labels good content: Promoted by any contributor, Certified only by people your admin authorizes.