#The Biology Part It appears that plants already do appear to communicate with each other and with animals, just not on the timescale of animals, and mostly via hormones. That being said, for something without a brain or muscle fiber, plants can react rather quickly. Acacia Trees, for instance, are known to react very quickly to grazers, producing a hormone which not only triggers tannin production in that plant, but in other nearby trees as well. Venus Flytraps, as another example, are quick enough to catch flies and other insects.
Anyways, the plants in question will need reason to be faster than they currently are. Are they predatory? That seems to be the reason why venus flytraps can act so quickly. Are there herbivores? Maybe they have something also slow moving that they're trying to avoid, so they develop defenses which act more and more quickly.
What about developing intelligence? Increasing Plant Perception will play a role in this. The developing intelligence, though, would require some sort of evolutionary pressure to do so. It could easily go hand-in-hand with dealing with predation or prey capture.
I would start by looking at a book and some articles. Specifically, the Communication of Plants and the academic article Rapid Changes in Tree Leaf Chemistry Induced by Damage: Evidence for Communication Between Plants to see evidence on how plants currently communicate, and if you can call any of those communications intelligence.
#The Social Part This depends on the structure of plants, and how detailed their communications could be. I imagine being intelligent and sessile while having others around you who are also intelligent and sessile would greatly influence the social-psychological environment of these plants. Specifically, I would think that you would go to great lengths to be polite, as there is no way to remove yourself from an unpleasant situation.