Nritta 
Nritta is pure dance or rhythmic movement of the body.  There are several intricacies of Nritta like the defined positions starting with  a 'Samapada' position.  There are innumerable combinations of adavus (the basic dance steps), the variation of foot movements. 

Nritya 
Nritya is the application of physical movement sin conjunction with the mind, a combination of rhythm and mind.  To express one needs a language.  The traditions have evolved a perfect system of gestures.  The basic alphabets of this gestural language begin with the single handed gestures and move onto double handed gestures.  These alphabets form words and then make sentences.  Expression comes from the mind and is shown through the face and eyes. 

Natya 
Natya is dramatic representation of stories from mythology.  The concept of dance actually originated in the form of dance dramas and later gained importance as a solo performance.  Even here the dramatic representation is prominent.  The solo dancer portrays different characters while narrating stories. 

All aspects of artistic merits are conjured up in Natya.  There is music for the musician, dance for dance lovers and drama for dramatists, beautiful line and picturesque poses for the painters and the sculptor and poetry for the poet.  Bharatha describes four kinds of dramatic presentations known as Chaturvrithi in Natyasastra.  They are Bharathi (expression through speech), Sathwathi (expression achieved through thinking and feeling), Kaisiki (the Lyrical, subtle movement for ladies) and Arabhati (an acrobatic, forceful movement to represent war, duels, etc.) 

This is the only system of art which exploits the body, the mind and the sentiments fully and brings an absolute co-ordination between all senses.  Without this absolute co-ordination it is not possible to convey the purpose of dance to the spectators.  The prime aspect is literary contribution.  The emotions are universal and common to all human beings.  these emotions are classified into eight categories namely Sringara, Karuna, Veera, Roudra, Hasya, Bhayanaka, Bibhatsa, Abdhuta and the ninth one called Shanta or tranquility. 

This quotation from the Vishnudharmottara Purana sums up the greatness of the art form. 
"To worship God by Natya is to fulfill all desire and to that one is unfolded the path of salvation.  The Dance gives prestige and longevity and destroys all misery.  The art gives guidance to the dull witted and increases the good fortune of humanity"