As you progress through the license classes, you earn more and more privileges. The Technician is limited to frequencies above 30 MHz. You'll be able to talk through satellites and experiment with digital modes. Local emergency relief is handled in this frequency range too. The General class gives you access to the frequencies below 30 MHz, which is also known as shortwave.
Worldwide coverage is a daily event on shortwave.
You also have access to all the modes and activities ham radio offers. Regional and international level emergencies are handled on shortwave, too. The Extra class is the jewel of the crown. Extra class licensees have all the frequencies available to US hams. There is a lot of fun for all classes of license.