This is a point where Moon is on its furthest point from the Earth. Perigee ("White Moon") - is the closest point.
This axes is activated when conjunct by a planet (either Perigee or Apogee in conjunction with a planet). Then the planet character will show what will trigger the axis.
IMHO The axis is an axis of comfort/discomfort or an axis of desire, Black Moon sphere usually being the point of desire to find yourself in but might some failure in. Usually Apogee is untrodden way, you karmically do not know how to realize yourself in it but might be attracted to it, or where you might do some mistakes due to not knowing better. This might indicate somewhat quest point. For example Apogee in one of the relationship houses might indicate loneliness in the sphere of this house' affairs, if aspected by a planet. This usually recognizes itself early in life. Later it might be solved. Perigee might be felt as "already found" or "already present so not very interesting", "karmically known or already trodden" in life in a way of the conjunct planet. Aspecting planets might be seen as "why" person is not accepted in the Apogee point. For example Uranus might mean being different to others in some way and that's why not accepted by society. Conjunction to Perigee making planet feel somewhat powerful and prominent, while conjunction to the Apogee making it felt somewhat problematic. Apogee might also show some gifts yet to be opened and path yet to be trodden and found yourself in, such as Lunar North Node.
I think such points might have lesser meaning than the planetary ones but can help astrologer if (only if) they are greatly aspected. A lot of minor aspect can show "inner layers" and karmic patterns that might help to further explain some other major things but not replace them.