Parallel of declination - This occurs when two planets are the same number of degrees of arc North or South of the Celestial Equator.
Parallel of latitude - This occurs when two planets are the same number of degrees of arc North or South of the Ecliptic.
The Parallel of Declination is a different kind of Aspect, because it does not refer to the Planets' longitudinal positions but rather to their positions in Declination (North or South of the Celestial Equator).
At either pole a planet on any parallel of declination moves along an arc parallel to the equator, to the horizon of the pole. It has neither ascension nor descension, but remains, day and night, above or below the horizon, according as it is in North or South declination.
A planet is inconjunct when it forms no aspect and is not in parallel of declination or mutual disposition to another planet.
The traditional astrological aspects - the conjunction, sextile, square, trine, and opposition - and parallel of declination, are important keys in determining weather patterns. The conjunction and parallel can fall into either category, depending on the planets involved.
The concept behind the use of Antiscion Points is that a planet crossing one side of a pair of antiscia will be on a point that would be in parallel of declination were it the Sun.
See also: What is the meaning of Aspects, Venus, Mars, Conjunction, House?