Usually it is considered that your left side symbolizes the receptive (perceiving) ability of the Universe while the right symbolizes the projecting force. It especially concerns to right-handed persons. Whether you feel, what you should become more susceptible and open?
The left side, or something appearing on the right or coming from the right, can represent:
Receiving or taking
Intuition
Creativity
Femininity
"Going with the flow"
Liberal political views (as in "left wing")
Negativity