It refers to the Universal Consciousness, that which is: 

1. Akhandit (complete, no boundaries, infinite) 

2. Not trapped within the cycle of rebirth 

3. Isn't burdened by the weight of Karma 

4. Doesn't possess Aham (concept of self) and the Ahankar (ego) that revolves around it. 

5. It has gained Aatma-gyan (self-realization).

Brahman, Param-aatma

Aatma that exists within you. It is :

1. Khandit (incomplete, has boundaries)

2. Trapped within the cycle of rebirth

3. Is burdened by the weight of Karma

4. May possess Aham (concept of self) and the Ahankar (ego) that revolves around it.

5. It has to gain Aatma-gyan (self-realization).

Jeev-aatma

It is the Aatma within someone else keeping oneself as the frame of reference. 

The minute one disrespects another, starts comparing oneself to another and passes judgement, then the former hasn't obtained Aatma-gyan.

Para-aatma

-Brahman, Param-aatma

-Jeev-aatma

-Para-aatma

State University of New York at Buffalo

Some refer to it as the soul, but when you dig deeper into its philosophy, it is refers to Consciousness. 
One is differentiated as living from the non-living when this consciousness awakens the hunger within the being. This consciousness awakens ones senses, thus allowing them to partake in this world and its associated materialistic life. 


Aatma

Pattanaik, Devdutt (2017), Devlok with Devdutt Pattanaik, Penguin Random House Publishing

Devlok with Devdutt Pattanaik

That which is Nirgun (has no form), Anaadi (from the beginning), Ananta (endless), specifically, that which is not bound by the concept of time, that has always existed and will continue to exist is called Aatma.

Etymology of Aatma

To understand the concept of Aatma, a poem was written in the Rig Veda, about 8500 years ago. 

There exist two birds, seated on a branch on a tree. One satiates itself by eating a fruit, while the other watches the previous eating the said fruit. 

This is a metaphor. The bird that is eating the said fruit is referencing one's body, that partakes in the intricacies of life, and uses its sense organs to enjoy every aspect of this life, while the bird watching the other is one's Aatma. 

There are three levels to this philosophy. 

One states that "I am observing you".

The other states that my Mann, bird 2 (mind) watches over my Shareer, bird 1 (body). In other words, "I am observing myself".

The third questions, "What entity watches over my mind?"

So the third level states that my Aatma (consciousness) watches over my Mann (mind), or "I am observing my own mind". In English, we may refer to it as recursion. This ability exists only in humans. This trait of observing oneself, as a witness, without getting emotionally involved, stems from the existence of Aatma. 

Rig Veda, along with Upanishads, also state that humans that search for Artha (meaning) to one's life, is moving towards Aatma-gyan (self-realization).

Vedic Philosophy of Aatma

Forms of Aatma

Aatma is referred to as Dravya, that which awakens your senses. It is that entity that carries the weight of Karma on its back.

Aatma in Jainism

Aatma doesn't exist in Buddhism.
Buddha preached that nothing lasts forever. Everything is temporary and everything should meet its end.
What one refers to Aatma, is in fact a reference to self, to one's identity and thus one's ego that has been carefully nourished over the years.

Learn Before

Related

Learn After