If you are used to Messages in iOS, you may have a problem using Messages on your Mac. Creating a new paragraph in a message on an iPhone or iPad is easy: Press the return key and you've got a new paragraph. That certainly makes for a nice organized and easy-to-read message.
Try the same thing using Messages on your Mac and the return key sends the message -- there's no consistency in the way the app operates on the different platforms at all. There is a workaround though: Instead of pressing return on your Mac keyboard, press the alt/option key + the return key. Bingo -- a new paragraph appears. It's not as intuitive as the iOS way, but you won't send messages inadvertently, or end up sending messages with long paragraphs.
Using the alt/option key will be a little frustrating at first, but after a while you'll get used to it. Apple has posted all sorts of other keyboard shortcuts here.
And now you know...