There are lots of different definitions for Domain-Specific Languages. This page groups some of them:

A DSL is a focused, processable language for describing a specific concern when building a system in a specific domain. The abstractions and notations used are tailored to the stakeholders who specify that particular concern.

- Markus Völter

A Domain-Specific Language is a custom language that targets a small problem domain, which it describes and validates in terms native to the domain.

- Domain-Specific Development with Visual Studio DSL Tools

In model-driven engineering, a Domain-Specific Language (DSL) is a specialized language, which, combined to a transformation function, serves to raise the abstraction level of software and ease software development.
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A DSL is a specialized and problem-oriented language [4]. Contrarily to a General Purpose
Language (GPL) (e.g., UML, Java or C#), a DSL serves to accurately describe a domain of
knowledge.

- DSL Classification , OOPSLA 2007