1. the state or fact of being present, as with others or in a place.
2. attendance or company..
3. immediate vicinity; proximity.
4. the military or economic power of a country as reflected abroad by the stationing of its troops, sale of its goods, etc..
5. Chiefly British. the immediate personal vicinity of a great personage giving audience or reception.
6. the ability to project a sense of ease, poise, or self-assurance, esp. the quality or manner of a person's bearing before an audience.
7. personal appearance or bearing, especially of a dignified or imposing kind.
8. a person, especially of noteworthy appearance or compelling personality.
9. a divine or supernatural spirit felt to be present.
10.British. Obsolete. presence chamber: the special room in which a great personage, as a sovereign, receives guests, holds audiences, etc..
The feeling was – most likely - reciprocal.