To date, messaging with Alexa has meant sending screeds using Amazon's in-house system, which doesn't do you much good if your recipient doesn't have an Echo speaker. You won't have to be quite so selective from now on, however, as Amazon has added support for SMS messaging through Alexa-capable devices connected to Android phones (there's no word on iOS). You can explicitly tell the voice assistant to "send an SMS," but it will also pick SMS automatically if you message a contact that doesn't have an Echo.
There are some catches outside of the Android requirement. Not surprisingly, you can't use this to text 911, participate in group messages or send MMS -- there's only so much you can do when you can't actually see the chats. You'll still be reaching for your phone most of the time, then, but this could be helpful if you want to let a friend know you're on your way while you're racing out the door.