יברכך יהוה וישמרך
יאר יהוה פניו אליך ויחנך
ישא יהוה פניו אליך וישם לך שלום
"May G-d bless you and watch over you. May He raise His countenance to shine over you and favor you. May He raise His countenance over you and grant you peace."
The latter two thirds of this blessing deal with His countenance and how "G-d makes His face shine upon you." Since imitatio Dei is such an important part of being a good Jew, what practical application does this concept have for us? Let's take a look at Pirke Avot:
Rabbi Shammai (Pirke Avot 1:15) tells us to greet every individual with a smile. Especially since Shammai was portrayed as stern, temperamental, and short of patience, why would he, of all rabbis, have given such an imperative?
For one, first impressions matter. If you have a scowl on your face when you meet someone, there is a good chance that it will be your last interaction. It's not simply a matter of the initial contact. It helps in keeping a relationship going, as is implied by Proverbs 15:1 when it says "a gentle reply turns away wrath, but a galling word excites anger." We are not only supposed to avoid arousing anger in others (Rabbeinu Yonah), but making sure that we ourselves do not get angry because anger is considered an evil trait (Bertinoro).
What happens if we don't feel like smiling? Although it would be great if we could be happy all the time, the fact is that we don't always do things in life because we want to do them. Sometimes, we are obligated to do so. Forcing ourselves to smile acts as an externality. Some might criticize this as acting phony. However, in Judaism, external actions are supposed to transform us internally (e.g., giving tzedakah is supposed to make us more voluntarily generous over time). Even when you are feeling glum, "faking it" helps keep your spirits up more so than wallowing in self-pity.
Whether you are having a good day or not, keeping a smile on your face affects the mood of those around you. Think about it conceptually: are you happier when you are around happy people or sad people? Happiness is contagious, and using that externality makes a difference. Both the Torah and Rabbi Shammai provide us with a necessary tool for successful human interactions. Let's use it to live happier and more fulfilling lives!