The Babel stones change the language of their holder(s) to gibberish, composed of mismatched language fragments. Furthermore, if (two or more) people hold the stones, they will be able to understand the new language as though it were their native language. The Warehouse is in possession of (at least) three of the Babel Stones, which are kept together on the inventory shelf in a leather suitcase.
In 13.1, the Babel Stones were used by Artie, Claudia, and Warehouse guest Douglas Fargo (of fellow SyFy series 'Eureka') to converse amongst themselves without having the Warehouse's back-up A.I. 'Hugo One' eavesdrop on them.
Real World Connections
The Babel Stones are from the Tower of Babel that is described in the book of Genesis in the Bible. People tried to build a tower so high it reached Heaven. To stop them, God changed all of their languages so that they couldn't communicate. That is what caused the different languages.