For instance, here is what Wikipedia has to say about Triplestore:
https://en.wikipedia.org/wiki/Triplestore
And here is DBPedia representation of it:
http://dbpedia.org/page/Triplestore
And here's how you'd get the data from DBPedia programmatically using SPARQL -
select * where { <http://dbpedia.org/resource/Triplestore> ?p ?o. }
Try it here - http://dbpedia.org/sparql/
Obviously, a triple store is a database that stores triples, and RDF (the Resource Description Framework) is an open standard maintained by the W3C so...
An RDF triplestore has the advantages of allowing for the storage of knowledge in a semantic way, that brings with it a powerful open standard for representing and querying the data.
If youre not familiar with graph databases and their uses at all tho, I highly recommend a little YouTube exploration on the topic. There's several conference presentations/sales pitches that get into the benefits and use cases for graphs in general. I just got exposed to it this year and it's been super interesting.