The main dish for Nowruz is Sabzi Polow Mahi (Sabzi Polow = Rice with fresh herbs, Mahi = Fish). In addition you have Kookoo/Kuku Sabzi (an Iranian Frittata made of fresh herbs and optionally barberries and walnuts). Besides this you have all kinds of sweets, some of them are depicted below:

Sources:

Tumeric and Saffron 1, 2, 3My persian kitchen 1, 2, Persian mama, Iran review, Bottom of the pot