The products
Power BI Desktop is the free Windows authoring tool — you connect, transform, model, and build reports here. Power BI Service is the cloud platform where reports are published, shared, scheduled, and secured. Power BI Mobile renders reports on phones and tablets.
Behind those, Power BI Report Server is the on-premises option for organisations that can't publish to the cloud.
Three engines, one file
A .pbix file contains three distinct layers, and confusing them is the root of most beginner trouble.
Power Query (M) runs at refresh time. It connects to sources and reshapes data before it lands. Everything here is about getting clean tables.
The data model (VertiPaq) stores those tables in a compressed columnar engine, along with relationships between them.
DAX runs at query time, when a user interacts with a visual. It computes measures against the model.
The practical rule: transform in Power Query, calculate in DAX. Doing row-level cleanup in DAX bloats the model; doing aggregation logic in Power Query makes it inflexible.
The workflow
Connect → transform in Power Query → load to the model → build relationships → write measures in DAX → design report pages → publish to the Service → set a refresh schedule → share via an app or workspace.
Most of the quality of a Power BI solution is decided in the middle three steps, before anyone draws a chart.