How
It is customary for the bride and groom to host pre-nuptial receptions shortly before the chupah ceremony. The bride hosts a women's reception in one room, and the groom hosts a reception for the men in a nearby room. Hors d'oeuvres, light refreshments, and l'chaims are served at both receptions. A more elaborate smorgasbord is traditionally arranged at the bride's reception.
At the Bridal Reception:
The bride sits on a distinctive, ornate throne-like chair. Her friends and family approach, wish her mazal tov and offer their heartfelt wishes and words of encouragement.
At the Groom's Reception:
Songs are sung, and often the groom — or another person present — delivers some words of Torah.
By many weddings, the ketubah (marriage contract) is also completed, witnessed, and signed at this reception.
In Chabad circles, it is customary for the groom to deliver a chassidic discourse which discusses the mystical implications of marriage.
Why
Separate Receptions: The custom whereby groom and bride do not see each other for the week prior to the wedding (until the veiling ceremony) necessitates the separate receptions.
Breaking the Plate: The irreversible act of breaking a plate is symbolic of the finality of the just-read tena'im.
Chassidic Discourse: The particular discourse recited contains ideas culled from the writings of all the Chabad Rebbes, and serves as an official "invitation" for these holy chassidic masters to join and bless the wedding ceremony.
What is the history of the tisch? I’ve always heard about what it is, but never how it came to be. I was always told it was an ashkenazi tradition.
There is no clear beginning date for the tisch. It appears to have begun at the outset of Chassidism, during the time of the students of the Maggid of Mezritch. It began as chassidim coming to their Rebbe's Shabbos meal on Shabbos afternoon, but soon developed into an event on its own.