Translation:Because it is very important that you write to me.
This site has a list of clauses that call for the subjunctive. Es importante que is one of them: http://www.studyspanish.com/lessons/subj1.htm
This site lists it as a "Impersonal Expression" which calls for the subjunctive: http://www.spanishdict.com/topics/show/68
I am asking the same question. Duolingo just marked me wrong for saying: "Because it is very important that you write me." Although your answer, and mine, are commonly used in speech in the MidWest of the United States, I am not sure whether we are grammatically correct in omitting "to" from the sentence. If anyone knows the answer to this question, please help.