Full clients verify transactions directly by downloading a full copy of the blockchain (over 150 GB As of January 2018). They are the most secure and reliable way of using the network, as trust in external parties is not required. Full clients check the validity of mined blocks, preventing them from transacting on a chain that breaks or alters network rules. Because of its size and complexity, downloading and verifying the entire blockchain is not suitable for all computing devices.
Recall that unique addresses are a proxy for the number of users, because they indicate how many non-zero Bitcoin addresses are in use. This metric has its strengths and weaknesses, which I wrote about here. Also, I have reviewed several other pricing methods which attempt to do the same thing using Metcalfe's Law. You can find those here and here.
Bitcoin is a digital currency created in 2009. It follows the ideas set out in a white paper by the mysterious Satoshi Nakamoto, whose true identity has yet to be verified. Bitcoin offers the promise of lower transaction fees than traditional online payment mechanisms and is operated by a decentralized authority, unlike government-issued currencies.
More recently, at a congressional hearing on Capitol Hill, global economist and New York University professor Nouriel Roubini said, "Crypto is the mother or father of all scams and bubbles." He called out "swindlers" who tapped into investors' fear of missing out and took them for a ride with "crappy assets that went into a bust and crash — in a matter of months — like you have not seen in any history of financial bubbles."