Hi Bibaswan,
Closed reference is when you take your sequences and cluster them against the Greengenes reference set - any of your sequences that don't hit and thus discarded.
Open reference is when you do closed reference, but instead of discarding the sequences that don't hit you cluster them at a certain percent identity to create de novo OTUs which you then try to assign taxonomy to using Greengenes.
De novo is where all sequences are first clustered by percent identity, then a representative sequence is used to assign taxonomy to the entire cluster.
Closed reference is the fastest, de novo is the slowest, open reference is in the middle. Which one to use depends both on your question of interest (i.e. are you interested in finding unique OTUs, or just comparing communities between say control and treatment groups), the number of sequences you have, and your computing power (and how much time you want to wait for your OTU table).
Luke