"This is a blue coat."
I'm very confused. The sentence before this one used この and this one uses これ. Why does the は move around when using this?
これ is used when "this" takes the place of a noun. It basically means "this thing." この is used when "this" is used to specify something, i.e. "this coat."
In the above sentence, これ is acting as the topic, hence the use of the は particle. It's because of this that in the English translation, "this" is acting as the sentence subject. You are stating that これ/this is a blue coat.
I don't know exactly what sentence you had before this, but to make something using この you might say このコートは青いです which means "this coat is blue." In a case like this, この is used instead of これ because you are using it to specify which coat. "This" coat as opposed to "that" coat. The は particle comes after このコート in this case because this is the topic, and the purpose of the sentence is to say that it's blue. "This coat" becomes the subject in the English translation in this case.
Wouldn't "青いコートです" be enough? "This" is pretty obvious, I thought about leaving it out.
That's just an example of how to use the word "これ" in a sentence.