A general top level domain (gTLD) is like .com and .net, compared to a country code top level domain (ccTLD) which is specific to a particular country like .us or .de . All of both kinds of domain names can be accessed by anybody on the internet.
For more information see: http://tldv.com/faq-information.htm
gTLDs are the older extensions that are not ccTLDs. Many of the newer extension are sTLDs which are "sponsored". The "g" stands for generic. Basically we are talking dots com, net, org, info and biz.
This is not an IDN so discussion should really be moved elsewhere, perhaps it would have been more useful if you had asked what an IDN actually is. It is seems that most Americans either don't understand what an IDN is or that they are fundamentally opposed to them, either because they don't understand them or because they mistakenly think that the the US owns the Internet and it should therefore be a US preserve.
Mercifully, the success of IDN no longer depends on convincing anyone from the US that they are a good idea. Frankly, most of the time, you would have more luck convincing Stalin of the merits of Capitalism.