Waxing refers to when two planets are moving farther apart (after conjunction and before opposition). Waning is when two planets are moving closer together (after opposition and before conjunction). They tend to indicate a building or dissipation of energy.
Waxing refers to when two planets are moving farther apart in their orbits (after conjunction and before opposition). Waning is when two planets are moving closer together (after opposition and before conjunction).
The most visible example of waxing versus waning is the phases of the Moon during the Sun-Moon cycle. As the Moon (moving faster through the zodiac) leaves the Sun behind after conjunction (New Moon), the Moon's light side becomes larger – this is a waxing Moon. After the Sun-Moon opposition (Full Moon), the light side becomes smaller – this is a waning Moon. The diagram at the top shows the 8 Moon phases, first waxing (right to left, over the top), and then waning (left to right, under the circle).
Generally, waxing indicates that energy is building, growing and developing. Waning indicates the energy is dissipating, integrating and being used for some purpose. You might think of waxing energy as being like inhaling, and waning energy being like exhaling.
Using the example of the lunar cycle, the waxing Moon is a time of building, developing and increasing energy, as the New Moon themes gradually take shape. During the waning Moon, this energy becomes assimilated and integrated into what we do; the energy gradually dissipates and the results and consequences of these lunar themes play out.
(Note that in the diagram, the line between light and dark moves from right-to-left, which is how it looks from the Northern Hemisphere. However, in the Southern Hemisphere the light/dark line moves from left-to-right. The diagram shows the progression of phases for the North. For the South go the other way around – under the circle first, the over the top.)
Lunar phases are a well known example of waxing and waning, but the principle can be applied to any pair of planets. So, a waxing aspect occurs between any two planets after their conjunction (0°) and before their opposition (180°). A waning aspect happens after the opposition and before the next conjunction.
Note that retrograde motion doesn't enter into this; nor is it important whether the aspect orb is applying or separating. What's important is that overall they're either moving toward opposition (waxing) or toward conjunction (waning).
Here's another example: we could say there is a trine aspect between Mars and Jupiter. This indicates an easy-flowing energy between Mars (action, assertiveness, impulsiveness) and Jupiter (enlightenment, confidence, understanding). For an added layer of interpretation, we can also look at whether the aspect is waxing or waning.
In the diagram here, Jupiter is in Aquarius, and a trine to Mars will be in either Gemini or Libra. If Mars is in Gemini, the aspect is waxing; we could say that confidence and sense of purpose are building. If Mars is in Libra, the aspect is waning; we could say that it's a good time to put that purpose into action.