So, yup, Cameron’s Avatar and Nickolodeon Avatar, the Last Airbender (the movie never existed. Period), actually had a common point: veggie communication networks. Yay!
In the first case, Na’vi were already physiologically equipped to connect to the Hometrees. In ATLA, both the Avatar (Aang and Korra incarnations) and Toph use the roots of an ancient Banyan Grove Tree to gain information about what happens on a different part of the world. In both cases, the overall idea was that the world, just like the trees, was one living organism where everything was connected.
Actually, the idea is not as crazy as it might sound. For a time, scientists have been aware of a mutual beneficial relationship between plants and (mycorrhizal) fungi, that grow around their roots and are known to promote overall plant growth. At the moment, they are evaluating whether they allow plants to communicate with each other to warn about coming insects attacks and, hence, prepare their chemical defense systems.
Scientists actually proposed that communication occurs through the release and detection of information-carrying chemicals that traverse the soil matrix through mycorrhizal networks (any brain analogy here?). In this sense, fungi, which are highly interconnected underground via their mycelia, conform a sort of plant Internet.
Image taken from Biology Pictures
This theory was tested by researchers from the University of Aberdeen, the James Hutton Institute and Rothamsted Research. They basically grew multiple sets of bean plants in groups. Some of these plants were connected viamycorrhizal networks, whereas others were kept purposefully isolated from the rest. Then, researchers infested single plants with aphids -a damaging insect-, and found out that clean plants connected to infected ones by the mycorrhizae built up their chemical defenses (i.e. release a chemical attractor for wasps, who feed on pesky aphids), whereas unconnected ones showed no chemical response.
There is also some evidence on airborne plant communication, i.e. veggie WiFi, so we can at least say that both Cameron and Konietzko did their homework right in this case.
Source: Ecology Letters