An eDSL is an (e)mbedded (D)omain-(S)pecific (L)anguage. In other words, it's a language for describing domain-specific entities and operations, that happens to be embedded into an existing (host) language rather than being given its own standalone parser, interpreter, compiler, etc. An eDSL gets to piggy-back off of the syntax and semantics of the host language, but extends it with domain-specific concepts in (hopefully) a way that integrates well with the host language.
Lots of things that are "just" libraries could also reasonably be thought of as eDSLs.
Lots of things that are "just" libraries could also reasonably be thought of as eDSLs.