...a (usually) formal symbolic language used to describe and reason upon constructs of another language.

Example: BackusNaurForm (BNF)

See: http://www.stcloudstate.edu/cgi-bin/foldoc.cgi?metalanguage

BackusNaurForm is a language (not a method) to formally describe the ''syntax''
of programming language constructs.

It is also possible to formally describe meaning or ''semantics''.
There are three classic ways to do this: AxiomaticSemantics (see http://www.foldoc.org/foldoc/foldoc.cgi?axiomatic+semantics) by using HoareTriple''''s, StructuralOperationalSemantics (see http://www.foldoc.org/foldoc/foldoc.cgi?operational+semantics) by GordonPlotkin, and DenotationalSemantics by DanaScott.

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The name of the FunctionalProgrammingLanguage ML derives from "meta-language," as the MlLanguage was originally a MetaLanguage for writing proof tactics for a theorem-prover.  Later people decided it was more generally useful.

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The term meta-language developed in 20th century philosophy as a kind of parallel to MrAristotle's Meta-physics (The book after Physics).

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The ForthLanguage can be used as a meta-language.  A Forth programmer can design an application-specific language, with whatever syntax and semantics are desired, and then write the application in that language.  Lispers express a similar attitude to programming.