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In this paper, we introduce the Age of Incorrect Information (AoII) as an enabler for semantics-empowered communication, a newly advocated communication paradigm centered around data's role and its usefulness to the communication's goal. First, we shed light on how the traditional communication paradigm, with its role-blind approach to data, is vulnerable to performance bottlenecks. Next, we highlight the shortcomings of several proposed performance measures destined to deal with the traditional communication paradigm's limitations, namely the Age of Information (AoI) and the error-based metrics. We also show how the AoII addresses these shortcomings and captures more meaningfully the purpose of data. Afterward, we consider the problem of minimizing the average AoII in a transmitter-receiver pair scenario. We prove that the optimal transmission strategy is a randomized threshold policy, and we propose an algorithm that finds the optimal parameters. Furthermore, we provide a theoretical comparison between the AoII framework and the standard error-based metrics counterpart. Interestingly, we show that the AoII-optimal policy is also error-optimal for the adopted information source model. Concurrently, the converse is not necessarily true. Finally, we implement our policy in various applications, and we showcase its performance advantages compared to both the error-optimal and the AoI-optimal policies.