To naturalize is to make someone a citizen of a country or to adapt to living in a new place or enviroment.
Naturalizing has several meanings that are all variations on the idea of becoming native. When an immigrant is naturalized, they become a full citizen of a country. Other types of naturalizing also involve foreign people or things fitting in. A foreign term — like adios — is naturalized because many English-only speakers use it. When something or someone is naturalized, they've learned to live and fit in somewhere new. They now fit in naturally.