Want an honest answer?

Onboard are >=2 bits of code. At least one of those is a specific system trained to recognize a "wake word". This specific system (ostensibly) doesn't send anything to an outside party. Its entire job is to recognize one wake phrase: Alexa, Ok Google, or Siri, and then if that wake phrase is used it responds and tells the second system to listen. As you can imagine, this is a pretty easy job to get right 80% of the time. So that can be put on a chip. So then it does its job, and it's the second system that sends everything to an internet service for whatever reason.

There are actually 2 processors in the devices. 1 that constantly listens for a keyword, Al la, Alexa, Hey Google. When it hears it it quickly spins up another "computer" that then sends your voice back and forth to the servers for processing and response. It's part of the reason that the listen word isn't easily customized.

On top of what the other person said, they are always listening. Amazon has provided audio from Alexa for the police