The breaking of the plate ceremony is traditionally performed at the tanaaim or vort as well as right before the "badecken" at the wedding. It is a custom to remind us in the time of our greatest joy that our happiness can only be bittersweet as we are still in galus. There is no brachah recited, the halachic witnesses requirements are not necessary for this and it is usually done after the signing of the tana'aim if indeed there is a tana'aim written at the vort.
The custom is that the two mothers break it together.
I have seen another reason, and that is the breaking of the ceramic plate signifies "a done deal". Just like broken ceramic cannot be repaired and is final, it symbolizes the finality of this transaction.
Wishing you a hearfelt Mazal Tov!