An MCP Server is a server that connects to an LLM and allows it interact with the "real world" (e.g. through the internet, files, etc.) by querying the MCP server.
In a similar way to how rules-based, programming language, computer systems interact with the real world through APIs and REST interfaces, LLMs interact with the real world using MCP Servers. The difference between an API server and an MCP server is that the latter is much closer to natural human language (though it isn't quite that, it appears more as a bag of words).