The alien race that communicates using metaphors is the Tamarians. Their unusual language is explored most famously in the Star Trek: The Next Generation episode “Darmok.”
The Tamarian language uses references to historical and mythological events instead of direct statements. Phrases such as “Darmok and Jalad at Tanagra” communicate an idea of two people overcoming danger together, while “Temba, his arms wide” expresses generosity or offering. The Universal Translator can translate the words individually, but it initially cannot explain the cultural meaning behind them.
Captain Picard eventually begins understanding the Tamarians after being stranded with their captain, Dathon, on the planet El-Adrel. Their language is sometimes casually described as metaphorical, but it also functions through shared cultural narratives, allusions, and implied logic. A common mix-up is calling them “Darmok,” but Darmok is the title of the episode and the name of one Tamarian cultural figure, not the race itself.