In the Power Editor, you can select a particular audience, such as the followers of your page, and have Facebook create a lookalike audience based on that. In other words, it analyzes the types of people in the audience you selected and creates another audience consisting of people with similar characteristics. It also automatically rules out anyone in the original audience so you are not just putting the same people on the second list.
You can then target this new lookalike audience with boosts or ads.
I am still learning about this and don't know exactly what criteria Facebook uses in creating the lookalike audience, but in the experiments I have done with clients, the lookalike audience does seem interested in the content we are putting out.
I should also add that I am targeting the lookalike audiences with pure content posts. In other words, I am not hitting them with a sales pitch. Instead I am targeting them with a song video (for the music clients) or a quote from the clients about their work (music or business clients).