The server monitoring part is already present since phpMyAdmin 3.5, but some of the parts were further improved in 4.0.
Server monitor (as you can see on picture above or on demo server) allows you to follow server status in real time. Besides predefined charts, you can choose to follow any of MySQL server status variables or some system parameters.
If you see something weird in the charts, you can select interval and inspect slow or general query log (if you have enabled it). This can help you finding most problematic queries for your server.
Advisor (on picture above or on demo server) is another way to improve server performance - it comes with extensive set of rules, which can help you tuning performance for your workload. Your server has to be running for significant time to give some reasonable recommendations (so don't expect these on the demo server, which is restarted quite often). However it is still recommended to read server documentation before doing any adjustments, as the setting might have some side effects, which will affect your workload as well.
Of course these are not magic pill to cure your unresponsive server, but can help you a lot in finding possible bottlenecks.