The break-in period is the first 30 nights of the 120-night mattress sleep trial. You must keep your new mattress for the full break-in period, but if you don't love it, you then have until the end of the 120-night sleep trial to return it for a refund.
As with a new pair of shoes, it takes some time for your mattress to break in. Sleeping on your new bed for 30 days gives you time to get used to the mattress and make an informed decision about keeping or returning it.