To put it very simply, the smart grid concept refers to various measures and tools around the physical power grid that help gain a comprehensive overview of the grid and its ecosystem, thus ensuring a reliable transport of electricity from all generation sources, centralized as well as decentralized, and allowing the two-way electricity flow between the grids and prosumers.
From this perspective, the “smart” element is rather about better ways for data collection, communication and analysis than about the advanced intelligence of the power grid per se. There are other interpretations of the smart grid concept as well. Most of these, however, refer to the grid as an independent, autonomous entity that is able to perform various actions on its own, which is currently not the case yet, that is why one should read such interpretations with a certain level of scrutiny.