I search for a website to learn German words of intermediate and advanced level, preferably not with translation, but with explanation in German. Vocabulary.com is the perfect example of what do I need. (German-to-English translation will be of no use for me, because English isn't my native language)
My proposal is Das digitale Wörterbuch der deutschen Sprache. After entering the search word, look especially in the upper left box for the definition.
There is Wortschatz bei the University of Leipzig. It is a corpora collection that automatically crawls online ressources and give example sentences.
They at the time of writing this have 26 Mio sentences and 425 Mio tokens.
There is also the web presence of Duden another often used dictionay in Germany. It may help you as well.
Edit: This web presence in only in german availibale, but that shouldn't be a problem for you.