The news is filled with stories about the Amazon Echo devices are spying on you. Well, that's overstated and ill-defined. (You've consented, so technically it's not "spying'.)
The Echo devices do indeed record what's going on in your room. They are constantly listening for the "wake word" that activates their processing. Unless you've changed it, the wake word is "Alexa." Determining if "Alexa" has been spoken takes place locally, on the device, so your recordings aren't constantly leaking out of your home.
But, if the device determines that you did say "Alexa" (even incorrectly) the recording of what you said after is sent to Amazon's servers for analysis. You didn't really think your $49 plastic computer was doing all the processing itself, did you?
In the Alexa app, you can set your Echo devices so that it plays a tone whenever it thinks the wale word has been spoken. This is well worth turning on because you will discover just how often the Echo mishears you. (Spoiler alert: very, very often.) And what you say following that tone is uploaded in a recording to Jeff Bezo's personal email.
Or maybe it's not. The problem with all of this is that Amazon, unlike Apple and even super-creepy Google, hasn't documented what they do with your recordings. You can go into the Alexa app and delete all your recordings (if you're able to figure out how) but there are no assurances that they are truly deleted. It's possible they're are only removed from the list you see. Unless and until Amazon becomes transparent about their practices, all you can do is hope and trust them.