This is a sentence from a report in the Economist.
Children who rebel may be threatened with being sent to stay with family in China, and they know from relations there that teenagers in America, even Asian ones, get off relatively lightly compared with those in China.
What does “get off relatively lightly” mean in this sentence?
get off
Escape a punishment; be acquitted
http://www.oxforddictionaries.com/definition/english/get-off?q=get+off
Get off relatively lightly means there was some punishment, but not as much you might expect.
In your example, the phrase means that American teenagers aren’t punished as harshly as Chinese teenagers for rebelling.
"teenagers in America, even Asian ones, get off relatively lightly compared with those in China" means that how teen rebellions in America are dealt with is less serious than in China.
Phrasal verbs like "get off" annoy non-native speakers of English to no end, since other languages use different structures to convey their meanings, and the phrasal verbs' meanings can vary by context.
