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Epoch means date and the term is used for a reference date/time, such as to indicate the point in time of an astronomical object's cited position within the celestial sphere; this is clearly necessary for stars that exhibit proper motion. A particular epoch as been chosen to be the current standard epoch for stated astronomical coordinates, J2000 epoch (aka J2000.0 epoch or epoch J2000.0), which is roughly January 1, 2000, 11:58:55.816 UTC. Citing equatorial coordinates with a J prefix (e.g., "J162702.56+432833.9", which for the purposes of this website, I've termed a J designator) indicates these are the coordinates for this object at this standard epoch. Previous standard epochs used in astronomy have been B1950.0 and B1900.0 with years 1950 and 1900. J stands for Julian date and B stands for Besselian date, which are based on a different specifications of the length of a year.
The difference between epoch and equinox:
Specifying a time as the epoch associated with an object's coordinates gives a time when some object was located there. Stars are moving relative to the Earth and Sun, showing proper motion, i.e., always changing coordinates, and for sufficiently-near stars, this change is easily noticeable as position-records are kept.
Specifying a time for the equinox of an object's coordinates is to define the coordinates, specifically to specify the position of the axes used by the coordinates. Axes of coordinate systems are based upon the position of visible astronomical bodies (e.g., the Sun), but these move relative to us with time in complicated ways, e.g., cycles. In particular, equatorial coordinates use the intersection of two planes, that through the celestial equator and that through the ecliptic. These change over time, e.g., the celestial equator follows the Earth's precession of the equinoxes. Therefore, to fully specify a celestial coordinate system, you specify the time of the equinox that it uses.
Another meaning epoch common outside astronomy is to indicate some designated period of time with some characteristic(s). This meaning is also used within astronomy, e.g., in the phrase epoch of reionization (EOR).