In 1953, Crick and Watson (with some help from Rosalind Franklin) determined the structure of DNA. But despite knowing what the molecule looked like (a double helix) and what it did (encode for proteins), nobody knew how, exactly, that translating and encoding happened.
There had to be, Crick had postulated, some sort "bilingual" molecule, an intermediary that could talk both to DNA and to the ribosome that created the proteins.
Ultimately he was right—that's exactly the job that transfer RNA does. But it took decades before anyone actually knew what tRNA looked like.
In 1956, Paul Zamecnik, a scientist working at Harvard, and his group of researchers made what one of them, Mahlon Hoagland, would later call "a fortuitous discovery." Hoagland says, in this interview:
Zamecnik himself and an associate of his discovered that the amino acids...not only were activated as I had discovered but were then subsequently transferred to an RNA molecule. This was a totally mysterious finding because there was no evidence that that RNA that it was attached to—had any role in protein synthesis at all.
What he's talking about here is how, in cells, the information from DNA gets transformed into the proteins, with amino acids as the building blocks and RNA doing the shuttling in between. This is how cells work—how life works. That little mysterious molecule doing the shuttling, it turned out, was transfer RNA.