Nothing but the place from where we are conducting testing
depending upon the development environment.

If the testing is done at the local environment to the
development team then we can call it as Localization

where as if the testing is conducting on site from the
development team then we can call it as Internationalization
testing

Localization:  It is a process of testing the local language
For Example: If your are testing ATM machine.It have local 
languages depends on the state. if that language is tested 
the it is called Localization

Localization testing is done on products developed in other 
languages other than English/local language.The products 
are developed in English & then translated into specified 
languange.So loacalization testing is mandatory.

Localization Testing:- For ex:- we have a client( china
clinet) who is requesting for an application to be developed
in china language. Here when we are testing the application
which is in china is called localization testing.

Internationalization Testing:- Now the same client wants to
release the same application in other languages like English
and spanish then development needs modification to the
application in such language and testing the application in
both the language then such testing is called
Internationalization testing.