There are the three ways in which God remains in this world:-
1)In Hinduism, Even you and I are the true avatar of God. Because Atman present inside our body is the reflection of God. Atman is not aware of its source due to the curtain of Maya.
When one get rid of Maya, he becomes God or Goddess himself in the human body.
2)For a special purpose he come on this earth to preach people or remove the excess negativity of this earth like Rama and Buddha.
3)Sakara(with form) manifestations of God that appears in front of us when we worship them. Like Demigods, demigoddesses, Shiva, Shakti, Ganesha, Paravathi etc.
Now to first of second points.
Simple body of humans and animals have 5 kalas. While incarnations come with extra kalas. Some Rama has 14 kalas. While Krishna is called Poorna avatara with 16 kalas. There are also anshavatars like Parshuram, Durwasa, Hanumans who have less than 14 kalas.
Description of 16 kalas are as followed:-
THE SIXTEEN KALAS
Five Kalas like 1) Anna Maya (with cereals), 2) Pranamaya (with breath), 3) Mano Maya (with mind), 4) Vigyanamaya (with knowledge) and 5) Anandamaya (with joy) are present in every human being. With little effort, humans can perfect in three more kalas - 6) Atishayini, 7) Viparinabhimi and 8) Sankramini. The other remaining eight Kalas are 9) Prabhvi. 10) Kunthini, 11) Vikasini, 12) Maryadini, 16) Sanhaladini, 14) Ahladini,1 5) Paripurna and 16) Swarupavasthit :
Anybody who has the ninth Kala besides the first five natural Kalas and next three perfected Kalas, becomes the god. As per scriptures, the ninth kalas Prabhvi means : KARTUM AKARTUM, that is able to do seemingly impossible tasks. Lord Narasinh is an example of this ninth Kala. Lord Narasinh has an altogether different appearance. He had a body of human and head of a lion. He appeared from a stone pillar that demon Hiranyakashipu had broken with a blow of his mace. It is not possible for an ordinary human being, only a God, having the ninth Kala Prabhvi, can do this. Among all these incarnations, only Lord Krishna is full of all the sixteen Kalas.
Very beautiful question in fact !