What it means
A lunar month has two halves. From new moon to full moon the Moon grows. This is Shukla paksha, the bright half. From full moon to new moon it shrinks. That is Krishna paksha.
Classical Jyotish treats a waxing Moon as a benefic and a waning one as weaker. The idea is simple. A growing Moon carries more light, and light is read as support: steady moods, family backing, public goodwill.
About half of all charts pass, so this is the easiest rule in the set to try. It is also a starting point. Several other rules here lean on the Moon, so it helps to know this about yours.
Do not read the waning half as bad luck. Tradition ties Krishna paksha births to depth, privacy and intensity. Different, not lesser.