Since the blockchain is public, how can we see it? The blockchain is a shared public ledger for Bitcoin. What does that mean exactly? Is it possible to see, publicly, all transactions? For every bitcoin a person owns, is he able to see all the historical transactions? If so, there should be privacy issues, no? If he can't, who can?
The blockchain is the decentrally maintained append-only log of all
transactions verified on the Bitcoin network. There are multiple websites, so called blockchain explorers that visualize this data on the web.

Indeed all transactions that ever happened on the blockchain are publicly visible, and looking at transactions on such a blockchain explorer let's you discover what transactions moved the same Bitcoin balance before you received it.

While all the transactional information is in the public, the involved parties remain private as they transact under pseudonyms called Bitcoin addresses. We can see time, volume, and involved addresses, but don't learn the individual's private information. 

However, through data mining observers may learn that some addresses are under the control of the same entity and might make some guesses about their usage.