This tab display the current log information & exists untill the server not restarted, as the server restarted this information becomes reloaded. For logging Solr uses Slf4j library & log4j.properties file.
While this example shows logged messages for only one core, if you have multiple cores in a single instance, they all will be listed with the level for each as shown below-
Here I used a term "Core", I'll discuss it separately. In logging tab you can select log level for your package or class. Just go over there in hierarchy & click you will get a list of all available logging level, select any one of them & logging for that particular package or class will starts automatically.