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An Expression in TouchDesigner is a text string that contains data (string, float, list, boolean, etc.) and operators (+ * < etc) that are evaluated by the operator's language (python or Tscript) and returns a string, float list or boolean, etc.
Expressions are used in Parameters, DATs (especially the Evaluate DAT), Tscript Commands and Scripts.
For Python expressions, see Python.
There is a Python expression execution engine to improve the perforamnce of Python expressions, read about it here: Optimized Python Expressions
For Tscript expressions, see Tscript Expressions.