to be present: to be here or on hand right now, whether a person who has arrived or a thing that is available in the moment
This is the plain, everyday Greek verb for something or someone being present. It is built from the ordinary verb "to be" with a prefix meaning "alongside," so it says that a person or thing is right here, at hand, in the immediate scene. Depending on what is present, English reaches for different words: a person "is here" or "has come," a moment "has arrived," a quality "is present" in someone, and the things that are present are simply "what you have."
With people it usually contrasts with being away. Paul leans on it constantly to weigh what he can do face to face against what he can only do by letter: when he is present he can act directly, when he is absent he writes. With things and abstractions it shifts toward availability: a time that is present has come, qualities that are present belong to a person, a message that is present has reached its hearers.
When the participle stands on its own as a noun, it names "the things that are present": the present moment as opposed to later, or the possessions a person actually has in hand. That is the same idea of presence, now pointing at whatever it is that is here.