To intone is to to chant in a flat voice. When you recite a poem you had to memorize in English class, you're likely to intone the lines without much expression.
You might intone bad news over the phone, bluntly and unemotionally, and librarians often intone a low command to keep the noise down in the library. People reciting prayers usually intone them as well. In the fourteenth century, the word was entunen, "sing, chant or recite," from a Latin root, intonare, "sing according to tone."