Specifically, the verb "to be" in its various forms (am, is, are, was, were, be, being, been) is often used to express existence.
Here are some examples:
* There is a book on the table. (is indicates the existence of the book)
* I am happy. (am indicates the existence of happiness)
* They were here yesterday. (were indicates the existence of their presence yesterday)
While other verbs can also imply existence, "to be" is the most direct and common way to express it in English.