Throughout ACP's help, we refer to J2000 versus local topocentric (equatorial) coordinates. It is assumed that you understand the basic astronomy coordinate systems:
If it were only that simple. The equatorial coordinates as seen from the observatory vary with location and time. The coordinates I would need to center a star here in Arizona tonight will be significantly different than those you would have needed from Australia or from here 5 years ago. Of course objects seem to move across the night sky due to the earth's rotation, but we're speaking of the equatorial coordinates, not the local horizontal coordinates! What causes equatorial coordinates to change?
The Wikipedia links above provide more information.
A catalog must be usable anywhere at any time. Clearly, we need a standard coordinate system (frame of reference) from which the coordinates for a given place and time can be derived. This is the International Celestial Reference System (ICRS), which uses the International Coordinate Reference Frame (ICRF). For all practical purposes, this is what we call J2000, which is geocentric and derived from the earth's axis (equinox) at Julian calendar 2000.0. You'll hear people talking about the "J2000 epoch" but to be proper, we should refer to the coordinate system as the "J2000 equinox". An epoch is a time reference only; our standard coordinate reference frame is based on the orientation of the equinox (earth's axis) at the epoch J2000.
In order to point the telescope accurately to an object, we need to "convert" the standard catalog (J2000) coordinates to those of the object as we see it from our location at the current time, called the local topocentric equatorial coordinates, or simply local topo. As originally stated, the apparent coordinates of an object change over time and with location on the earth. Some research-grade telescopes do the conversion within their own control systems, but the vast majority of telescopes used with ACP do not. Therefore, ACP normally does this conversion for you, leaving you to (conveniently) work in J2000 coordinates for your observing plans. If you're interested in the details, read on.
As outlined above, there are several factors that influence the variation of the apparent equatorial coordinates at a location and time. To convert from J2000 to local topo involves several steps (this is simplified, omitting the very tiny corrections, which ACP nonetheless applies!):
At this point we have local topo (assuming "tiny" corrections have been omitted). We can transform to local horizontal (alt/az) and apply the refraction correction, then back to equatorial (if we have an equatorial mount) and point it. If you hear someone talk about JNow coordinates, be wary. This term is often imprecise, including only the first two corrections above, or maybe all four (and maybe the tiny ones too).
In any case, all coordinate input to ACP, whether it comes from a Deep Sky Catalog search, from positions you take out of specialized catalogs, or from MPC or NEO listings, must be J2000 coordinates. ACP will perform the appropriate calculations to ensure every image is centered.