Magazines can be read directly on your website with so called "embeds". These embeds use an iFrame or Javascript and load your whole magazine onto your website.
Tutorial Video
Tutorial
First go to "My Publications".
Then click on the "little pen icon" to edit your magazine.
Scroll down to the section "Embed" and click on "Open Embed Options".
Then the "Embed Wizard" will open up.
Here you have the choice between several types of embeds.
Learn more about the settings of all embed types here