I was curious, the DS-7608NI-I2/8P supports two hard drives - does this mean that if I installed two drives, I would have double the space or is it meant to offer redundancy?
Generally, yes, that would be the case.
On other models in that series with more drive bays, there are configuration options to create various levels of RAID array if protection from failure is a key requirement.
Yes, it extends your storage capacity. Another huge benefit to using more than one drive, is the feature that lets the drives sleep! Meaning any drives that are not being written to will stop spinning. This greatly increases drive life.