I have read all kinds of info on what moon phases do what, but I am at a loss as to why. Why does a full moon have more power than a waxing moon, and why is a waning moon good for sending stuff away? I dont understand how the power differs depending on how the suns light is reflected off of it.
Its just symbolism. When it is waxing, the light is increasing, therefore things that you do to gain things will use this symbol. When it is waning, the light is decreasing, therefore things that you want to decrease or get rid of will use this symbol. On full moon, you have a full amount of light, therefore everything will be at its fullest ability. On the new moon, you have no light, therefore it is for either new beginnings (as this is the beginning of a new lunar cycle) and/or everything is at its weakest.
Honestly, it doesn't matter beyond symbolism because the whole moon is there all the time. ;)