It refers to a type of language which does not show any excitement or feeling. Sober, parco, serene or plain language. A judge's own language. Concise, brief.
Concerning the laconios, natural of Laconia ( region of the ancient Greece where he was 41 Sparta; The Spartans were terse and concise to talk, so this adjective became a way to appoint people of few words.
kind of language as well as: legal, brief, concise, and so on.