DAX or "Data Analysis Expressions" is a new language that was introduced with Microsoft PowerPivot. It is a formula language which allows users to define custom calculations in PowerPivot tables and Excel Pivot Tables. It includes some of the known Excel formulas and adds functions that are designed for PowerPivot to work with relations between data and perform dynamic aggregations.
The syntax is very similar to that of Excel formulas, but DAX is meant to work with tables and columns where Excel uses ranges. DAX formulas are highly performant because they make use of the in-memory VertiPaq engine, making it easy to rapidly perform these calculations for several millions of rows.