Most often, the writing that students do in school is simply for the eyes of the teacher.
Interactive writing involves students writing to and with other students.
There are a number of reasons why this might be useful. Secondly, writing with other students can give them a clear focus for their work. Interactive writing will involve them in asking each other about grammar, spelling, vocabulary, phrasing, etc. While students are working in groups, you can circulate around the class, reading what they have written and helping with any problems. This may not be a problem since one of the purposes of interactive writing is to enable students to exchange ideas.