There are two mitzvot that have significance with the outside of our homes—the Chanukah menorah and the mezuzah. However, the similarities end there. The menorah is intended to bring the light of the Chanukah to the outside world, while the mezuzah is intended to be at the entrance to the inside of the home.
Here is a way to better appreciate the difference between the two: placing the mezuzah on our doorpost is a positive act that we do to bring positivity into our homes. On the other hand, the main purpose of placing the lights of Chanukah toward the outside is to disperse the darkness of the world, to keep the darkness away.
However, the most productive way to keep negative factors in our life and in the world around us away from us, is by being active, by doing something, by doing a mitzvah. This way we have both benefits—we have the benefit of keeping the outside (negative) darkness out of our life, while at the same time we bring light into the world.
This is what the lights of Chanukah are all about. Creating positive waves.
A bonus detail when it comes to lighting the menorah outside our home is that people who light it at their door outside (in places where the weather permits) also light it on the left side of the door, while the mezuzah is hung on the right side (when entering a home). This also signifies the difference between the mezuzah and the menorah. The right represents the positive act and the left represents the withholding of negativity in the world. Lighting the menorah ensures the evil in the world will not take hold.
As we light our Chanukah candles, let us keep in mind to not only illuminate the world with kindness but also to rid the world of negativity.
Shabbat Shalom and Happy Chanukah