Love
Love is a theme that manifests in the relationship between Jake and Neytiri. The two of them seem to be enemies from the start, but even in their aversion to one another, we can see that there is a spark of chemistry. This blossoms into a full-blown connection as they spend more time together. When the time comes, and Jake must choose a mate, he and Neytiri already know that they are meant to be together. Their love is not only a connection of the hearts and body, but a spiritual one, and in lieu of saying "I love you," they tell one another, "I See you."
Exploitation and Extraction
The film is about the Earth's RDA (Resources Development Administration) coming to Pandora in order to mine it for the richness of its resources. The organization justifies its exploitation and extraction of resources as being in the best interest of the people from Earth, but it is an act of violence, not only against the Na'vi people, who live on Pandora, but of the planet's environment itself, a complex and diverse biome of various interconnected flora and fauna. This theme bears resemblance to colonization and the pillaging of environments and indigenous structures as it occurs in our own world.
Indigeneity
The Na'vi are the group that is native to Pandora, and as such, they are trying to protect their home from invaders. Thus, a major theme in the film is indigeneity and the sanctity of native boundaries. The RDA, equipped with high-tech, destructive equipment, seek to move the Na'vi or use military force to move them, citing the power of their weapons as reason enough for their entitlement. A major conflict in the film is the one between the brutish military and the indigenous Na'vi population, who are protective of their home and want to keep it for themselves.
The Power of Nature
While the RDA wants to extract resources from Pandora, the Na'vi live in harmony with their tropical home. They have a symbiotic relationship with their lush and resource-filled home that gives them a special connection to the plant and animal life on the moon they call home. When a giant battle ensues with the RDA, the Na'vi get some much-needed help from the animals of Pandora, who charge onto the battlefield and provide crucial help in the fight against the "Sky People" (humans). In this moment, the Na'vi's close bond with the natural world serves them and comes to their aid.
Spirituality
There is a spiritual component to the abundant natural resources of Pandora. The Na'vi people have a strong connection to nature by way of their belief system. After they kill a living being, they say a prayer over its body, and they believe in signs and omens, all presided over by their goddess, Eywa. Eywa is based in the root system that connects the trees of Pandora, and serves as a kind of spiritual database, a divine feminine order that presides over all beings.
Science
Avatar is not just a film about the conflict between the Na'vi and the humans who are trying to colonize their home, but also about the conflict between science and the military. The RDA is on Pandora for the purpose of extracting resources from the environment, but the scientists are there to learn more about the Na'vi and the botanical world of Pandora. These two goals are in direct conflict with one another: the ruthless and mercenary goals of the military, and the peaceful, inquisitive goals of science. Science, the work of Dr. Augustine and the others, is depicted as a force for good, something that creates connection between disparate groups, leads to education and diplomacy, and could potentially be integrated into life among the Na'vi on Pandora.
Destiny
Another theme in the film is the notion of destiny. When Neytiri first rescues Jake from the creature, she wants to shake him off and abandon him, as she is mistrustful of the fact that he is not a Na'vi. However, when seeds from a sacred tree surround Jake, Neytiri interprets it as a sign and changes her mind. In this way, Jake is depicted as destined to integrate himself with the Na'vi. This is confirmed when he is able to become a warrior and even tame the notoriously difficult toruk. These events serve as sacred signs of Jake's status as a hero of the Na'vi, a predetermined role.