The @Library annotation in Jenkinsfiles tells Jenkins to load shared library code before running the pipeline. The underscore (_) after the annotation is important because it instructs Jenkins to import the library functions immediately, making them available in the pipeline script. The execution flow starts by reading the Jenkinsfile, detecting the @Library annotation, loading the shared library, then running the pipeline stages that can call library functions. Variables like 'libraryLoaded' and 'myFunctionAvailable' change from false to true once the library is loaded. If the library name is wrong or the underscore is missing, the pipeline will fail or the functions won't be available. This visual trace helps beginners see how the annotation affects pipeline execution step-by-step.