In ArcMap you are using query's in
Query expressions
Query builder (Select by attributes, Definition query, label classes etc.)
Label Expressions (VB Script or Jscript)
Calculator expressions (either VB Script or python expressions)
Most of the expressions are built upon Structured Query Language (SQL) in a kind of "where clauses" like <field_name><operator><value>, so perhaps you should start by reading something about that. It's to difficult or complex for me to explain here.
Further more there is different syntax variations depending of, if you are using it on data in a personal-, filebased- or SDE database.