The line is credited to Frank Smith (1928–2020), the psycholinguist best known for his work on reading, and quotation sites link it to his 1990 book To Think. We could not open To Think to confirm the wording or page, so we list it as attributed. It means one language keeps you on a single path, while a second opens many others.
What it means
With one language you move through life down a single corridor: you reach only the people, books and ideas that language leads to. A second language adds doors all along that corridor, to other people, cultures and ways of seeing.
Where it comes from
Frank Smith was a psycholinguist who wrote widely on reading, thinking and learning; To Think (1990) is one of his books. Quotation sites credit this line to that book, but none of them gives a page, and we were not able to see the book's text. We therefore cannot confirm that the sentence is in it, or in exactly this form.
Quotation sites and English-teaching materials credit the two sentences to Frank Smith, and we found no evidence that the line came from anyone else. Until the passage is located in Smith's own writing, it is best described as attributed to him.