To "remain in the natural state" refers to the fact that generally, like now, you experience the arising of the mind, which is the constant flow of concepts or conceptual proliferation, that arise and subside, arise and subside. Through objective appearances and subjective awareness, you experience the conceptual proliferations.

So when you sit in equipoise and attempt to remain in the natural state, you are looking in, turning in, you are no longer focussing externally. You turn inside and then simply relax.

"Simply relax" means that you don't think of a single thing. You don't generate faith or fervent regard, or give rise to virtuous thoughts, or have some devotional thought for the guru, nor do you stop thoughts, or change or obstruct them. You don't do anything other than just simply relax.

In that state of simple relaxation, the arising of thoughts or concepts is naturally arrested, severed, as if cut off with a knife. In the moment of that experience, there is no experience of thinking about the past, anticipating the future, or being distracted in the present. One simply remains in the natural state.

-- Yangthang Rinpoche