The alien race that communicates by referencing historical figures is the Tamarians. Their language uses brief allusions to stories, legends, and events from Tamarian history rather than direct statements.
This idea is explored in the Star Trek: The Next Generation episode “Darmok,” in which Captain Picard struggles to understand Captain Dathon. Phrases such as “Darmok and Jalad at Tanagra” refer to a historical meeting between two figures who became allies after facing danger together. “Temba, his arms wide” expresses generosity through another cultural reference.
The universal translator can render the individual Tamarian words into English, but it cannot automatically explain the cultural meaning behind the references. That is why the Tamarians initially seem incomprehensible. The common mix-up is to identify “Darmok” as the race; Darmok is one of the figures in the story, while the species is the Tamarian race.