It’s not a word that rises unbidden to the lips of English speakers today, nor — if the record is to be trusted — at any time. It means a thing without value or use. It was borrowed from French, where it may still be found in dictionaries, though firmly marked as literary. According to the lexicographer Emile Littré, who compiled a famous dictionary of French in the middle decades of the nineteenth century, it’s a bastardised form of the Latin breviarium, the source of breviary for the service book used by Roman Catholic priests.
The link had been explained by another lexicographer two centuries earlier. Randall Cotgrave wrote in his French-English dictionary of 1611 that the word came to mean “foolish charms or superstitious prayers, used by old and simple women against the toothache, and any such threadbare and musty rags of blind devotion”, hence something valueless. A rare appearance is in a letter of 1786 by the writer Fanny Burney, in which she refers to “Talking to your royal mistress, or handing jewels ... and brimborions, baubles, knick-knacks, gewgaws”.
It is much less weird in German, in which the closely connected Brimborium, also borrowed from French but given a Latinate ending, is an informal term for an unnecessary fuss. The sentence “du machst viel zu viel Brimborium um eine Kleinigkeit” might be translated as “you’re making a lot of fuss about nothing”.