So does this mean they'll only censor them in a certain country when that country's government asks them to do it, or also when the US Government asks them to censor them in that country?
A country can only ask Twitter to censor the information in that country. For example, if Germany doesn't want the German people see pro-Nazi content, they can ask Twitter to censor it in that country. Twitter will then report it in to http://www.chillingeffects.org/.