One might write to a senator about some issue that is before the senate for consideration. If one was writing to a United States senator, perhaps it might be about the president's nominee for the Supreme Court, which the Senate is blocking, for example. If you are writing to a state senator, about some issue before the state legislature that is in the news. One might write to support or oppose a position the senator has taken and explain why. One might write about an issue that is of concern to you, such as gun control or the Affordable Care Act or anything else that might be controversial. One might also write to invite the senator to be a speaker at an event, such as high school graduation or some such thing. There might be any number of reasons to write.
