The simcha is the realization that even though we now understand the depth of what we have gone through and the potential problems that we have caused ourselves, Hashem is now saying, "Come and be with me and understand that I have forgiven you."
It is only now after Yom Kippur that we can actually feel the simchah of the gmar din (whether for good or better) that has been signed on Yom Kippur and will be sealed as a result of ivdu es hHashem Besimcha. After all the tochcha says that we would be punished because
You did not serve Hashem besimcha
Happy Days Are Here Again
The Hebrew word simchah shares some of those senses. But it goes
deeper. The Sefer HaCarmel (Malbim) differentiates between gilah and
simchah. "Simchah indicates an inner heartfelt joy that is constant."
Citing the verse (Psalms 31:8) "I will exult (agilah) and rejoice
(esmechah) in Your kindness ..." the Malbim explains that gilah
connotes a sudden burst of delight. Then he relates it to a verse in
Isaiah (25:11), "This is G0D; for Whom we hoped; let us exult and be
joyful with His salvation."
The Alter Vorker Rebbe (d. 1848) explained this with a story: A king
came through a tiny village with his royal procession. One young boy
was so unnerved by the spectacle that he threw a rock at the king's
carriage.
Immediately, soldiers rushed to catch the boy and were about to kill
him. But the king shouted, "Don't harm him. Take him with us back to
the palace."
In the palace, the king arranged the finest teachers for the boy.
After 10 years, the king sent for the boy - now a young man. As he
entered the throne room, the young man bowed low to the king, then
stood in reverential silence.
"Do you remember," asked the king, "the day we first met, when you
threw a rock at my carriage?"
The young man was seized with shame and fainted.
After Yom Kippur, the Vorker explained, we are like that young boy. We
spend 10 days coming closer to the Divine, until we reach the pinnacle
of Ne'ilah. Then, at Maariv, we suddenly realize, "Oy! What have we
been doing all year!?" And we pound our hearts in shame and ask for
forgiveness.
So where do we get the joy?
Rabbi Shlomo Carlebach (d. 1994) said
Like the boy who suddenly realized in shame, "What have I done?!" -
after Yom Kippur, we can be left feeling we have no place in this
world anymore.
But the Divine says, "Come; come with Me. I have a place for you, a
place to shelter and protect you."
That place is called the Sukkah.