The Zohar calls the highest point of Shabbos in the late afternoon, raiva deraivin – the time at which HaShem's innermost will is revealed. At that unique moment, after Mincha, chassidim would gather to sing niggunim and listen to a maamar of Chassidus in order to experience this kedusha, and enable it to inspire and empower them throughout the coming week.
(סידור עם דא"ח – סדר סעודה שלישית, אג"ק חי"ד ע' קיא, סה"ש תנש"א 664 'ב ע"ח)
During one of his many travels, the Baal Shem Tov once spent Shabbos together with his talmidim in a little village. As the holy day drew to a close, the local innkeeper gathered all the Yiddishe villagers to join his guests at the table, where they all partook of a generous Third Meal and sang niggunim of praise. Seeing that this occasion was accepted so warmly Above, the Baal Shem Tov asked his unlearned host why he chose to honor the shaleshudess meal so lavishly. The man explained, "I have heard people say that they want their neshama to leave their body while they are among Yidden. I have also learned that on Shabbos, every Yid has an additional neshama – so every Shabbos I want my additional neshama to leave me in the company of fellow Yidden."
Hearing that response, the Baal Shem Tov was visibly pleased.
(כתר שם טוב אות שפו)
Once, during the years that the Frierdiker Rebbe was in Otvotzk, Poland, he complained to one of his chassidim, "How can it be that at the very time when raiva deraivin is revealed, a yungerman can sit and munch on grapes with his legs crossed?"
(בכל ביתי נאמן הוא ע' 66)
The Frierdiker Rebbe writes: There will come a time when everyone will recognize the complete truth – that the happiness of a Yiddishe home depends on keeping the holy Shabbos.
(אגרות קודש מוהריי"צ ח"ה ע' רפב)
CONSIDER
What is the reason for additional learning on Shabbos: the extra time available or the holiness of the day?
Why should the happiness of a Yiddishe home depend on Shabbos?