That's a really good website, but try to start with small Airports, or Airports in Europe even in Spain. They speak both English and Spanish, what happen in aviation is easier if you know the procedures, and it depends on which frequency you are listening, if you listen clearance (you have to know the taxiways of the airport), tower (you have to know which kind of procedures are in the 5 nautical miles radius), approach, departures, terminal. (it all depends). There's a social red of virtual pilots called Vatsim, www.vatsim.net if you have flight simulator and you have some knowledge in aviation. You can be able to fly with people who plays like ATCs. Tambien hablo espanol si necesita alguna ayuda :) !!!

I have not used the website you mention, but I work in the industry. The problem is the phrases are very specific to the ATC environment, usually spoken very quickly, often referencing reporting points, beacons, etc. that will not mean a lot unless you are familiar or have a map of the specific airspace and routes they are talking about. Even then, it is sometimes difficult to understand unless you know what you are expecting to hear. If you have any specific examples of phrases or words I will try and explain them.