にほんごで メールを かきます / I write mail in Japanese.

にほんご

means "Japanese language.".

にほんごで

"で" is a method marker. So, it means "by Japanese" which is "in Japanese" in proper English. You can use "で" to express what language or character type you use to do the action.

にほんごで　メールを　かきます

"めーる/ mail". "かきます/ write". This means "I write mail in Japanese.".

えいごで　はなします

"えいご/English", "はなします/speak, talk". This means "I speak in Enlish.".