Many plants, such as Mimosa pudica (the "sensitive plant"), employ electrochemical signals known as action potentials (APs) for rapid intercellular communication. In this paper, we consider a reaction-diffusion model of individual AP signals to analyze APs from a communication- and information-theoretic perspective. We use concepts from molecular communication to explain the underlying process of information transfer in a plant for a single AP pulse that is shared with one or more receiver cells. We also use the chemical Langevin equation to accommodate the deterministic as well as stochastic component of the system. Finally, we present an information-theoretic analysis of single action potentials, obtaining achievable information rates for these signals. We show that, in general, the presence of an AP signal can increase the mutual information and information propagation speed among neighboring cells with receivers in different settings.