Heidegger tries to answer this question in Being and Time. Heidegger uses the word Dasein that was previously used by Hegel to signify existence, and he talks about how Dasein is being-in-the-world. Thus from Heidegger’s perspective it is Dasein that exists in the world. But that existence is not like the existence of things, because Dasein is an ecstatic projection of existence that brings the world into being. The word Existence is related to the word ecstasy. But there are different kinds of modalities of being-in-the-world called Present-at-hand and Ready-to-hand. And thus Dasein is normally changing modalities as it interacts with things in the world. However, all these modalities and more discovered later by Heidegger and others are part of the ecstatic projection of dasein that is a natural part of the human being. Thus what exists in the world first and foremost is Dasein because it is through Dasein’s existence, throwing forth the world that the world itself exists for Dasein to be part of.
Quora answer: What exists in the world?