A configurational language is typically characterized by its rigid phrase structure rules, determined by the underlying sentence structure. This results in a hierarchical tree structure that is ordered according to the language’s syntactic structure and may undergo syntactic movement.
In contrast, non-configurational languages tend to have what is called a flat phrase structure instead of a hierarchical ordering.
The configurationality of a language may be determined by a number of factors including the predictions of binding conditions as seen in the work of Lai (1998).
Lai, I. S. (1998). The grammar and acquisition of Secwepemctsín independent pronouns. [Master’s thesis, The University of British Columbia].