The line is widely credited to Flora Lewis (1922–2002), the New York Times foreign-affairs columnist, but we could not find it in any column, book or interview of hers, or in any reference work that gives a source; it circulates on quotation sites without citations. It means a new language teaches you a new way of seeing, not just new labels.
What it means
A language is not a set of new labels for the same objects. Each language divides up the world and expresses relationships in its own way, so learning one also teaches you to think along different lines.
Where it comes from
Flora Lewis was an American journalist who spent most of her career abroad, reporting from London, Warsaw, Bonn, Paris and elsewhere, and she was the first woman given her own column on the New York Times op-ed page. The sentiment fits a multilingual foreign correspondent, and the line may well be hers.
But every appearance of it we found is on a quotation website or a language-learning page, none with a publication, date or occasion. It has no Wikiquote entry, we found it in no reference work, and a full-text search of the Internet Archive's digitised books turned up no printed source. Until a column or interview is found, it is unsourced: credited to her, not traced to her.