Google states that the Google Assistant (the personal assistant that runs on the Google Home, Pixel and the Allo app) uses 'conversation history' for targeted advertising:
Does Google use my conversation history to personalize the ads I see?
If you interact with the Google Assistant, we treat this similarly to searching on Google and may use these interactions to deliver more useful ads. You can delete past interactions with your Assistant at any time.
What exactly is Google using when it says 'conversation history' - is Google Home listening to everything so it can target advertisements or are my queries only stored after saying 'OK Google'?
Some sources suggest that the Google Home might even be recording what I listen to on the TV:
"That microphone will be a witness to every verbal interaction in the home. It will also know what you watch on TV, what you listen to, and, obviously, when there's no one home."