There are several important languages that can be used with Analysis Services, including:
DMX
MDX
DAX
XMLA
Data Mining Expressions (DMX), as the name suggests, is a language used with Analysis Services to work with mining structures and mining models. You can use DMX to to create new models, train the models, and browse the data.
Multidimensional Expressions (MDX), is a querying language that you can use to work with Analysis Services for browsing and querying multidimensional data stored in the cubes. You can not only work with the cube, but also with dimensions, KPIs, and other features of the deployment.
MDX is based on XML for Analysis, which is a markup language used mostly for configuration of Analysis Services. You can use XMLA for backup, restore, or any movement of data.