Because of its shape and its branches which fall down to the ground, a willow tree is often associated with sadness or, in some cases, with eternity (branches pointing down back to earth).
They are also a symbol of resonance and harmony.
Willows generally grow in place nearby water. In Celtic culture, they are linked to the moon and magic (and places for ceremonies intended for enhancement of psychic abilities, that honour the moon as well as increasing the essence of love in our lives).