to be: the plain verb of being, used to link a subject to what is said about it, to say that something exists, and to say where someone is.
This is the ordinary Greek word for to be, and it is one of the most common words in the New Testament. Most of the time it does the quiet grammatical work that English does with is, are, was, and will be: it joins a subject to a description. "This is my beloved Son." "Blessed are the poor in spirit." In a sentence like that the word carries almost no weight of its own; it simply ties the two halves together.
The same verb can also make a stronger claim. It can say flatly that something exists, as when Hebrews says anyone who comes to God must believe that he is. And it can say where someone is or that they are present, as when the angel tells Joseph to stay in Egypt or when the disciples ask the risen Jesus where he is staying. These are not different words, just the one verb pressed into the three jobs of connecting, existing, and being present.
One special use stands out. In John's Gospel Jesus repeatedly says "I am" (in Greek, ego eimi). Sometimes he completes it ("I am the bread of life," "I am the good shepherd"), and sometimes he leaves it hanging in a way that startles his hearers ("before Abraham was, I am"). Here the plain verb of being is doing something far from plain: it points to who Jesus is, and it echoes the way God names himself in the Hebrew Scriptures.
So the range of the word runs from the most colorless grammar to the most loaded claim in the Gospel, all from a single verb. The reader's task is to let the sentence, not the dictionary, decide how much weight it is carrying.