Something emblematic is symbolic. Empty buildings are emblematic of a city in decline, and a crown is emblematic of royalty.
If you know that an emblem is a visual symbol, then you won't be surprised that emblematic things stand for other things. In fact, the word emblem comes from the French word for symbol. Something emblematic represents a larger issue, good or bad. Sometimes emblematic is used for things that are excellent examples. An A student is an emblematic student, and a war hero is an emblematic soldier. Emblematic people are symbols of what others aspire to be.