For those have not been into Bitcoin or cryptocurrency, the "blockchain" is essentially a distributed ledger of all (in the case of Bitcoin) Bitcoin transactions. So when Bob send Bitcoins to Fred, there is a record, and this record is recorded on servers (or nodes) all around the world.
There is also a very clever mechanism, mining, which verifies all these transactions, so Bob cant send the same bitcoins to Fred and John at the same time.
It is a work of genius.
However, the system lends itself to money laundering. Although there is complete transparency around all the transactions, Bob and Fred are just anonymous entities, they could be anyone (or anything) located anywhere in the world. Changing identities is as simple as pushing a button. There are also no limits on the size of any transaction, whereas banking systems look closely at transactions greater than $20 million.
To put some scale on money laundering, annual estimates conclude it is in the vicinity of 2-5% of the global GDP, or about $1 trillion a year. The entire bitcoin valuation is only $4 billion, so you can easily imagine that so far bitcoin has been merely used as an occasional laundering experiment, some playful R&D. This is why folk such as Putin aren't really batting an eye.
To counter this system of anonymous financial transactions, early adopters are suggesting that to bring Bitcoin and the Blockchain mainstream, we need its users to be validated and authenticated.
I am not sure exactly how this could work, as no one would want their personal details (name and location) visible in the Blockchain. There would need to be some sort of authentication agency set up like ICANN to manage and assign ID's, with only the new ICANN able to map the ID back to its authenticated user. I think several global banks are interested in assuming this role, but they will fail (Citibank), like the Telco's did in coming up with something before Apple Pay launched.
However, with governments around the world (most recently Russia) starting to kickback on having data stored about their citizens on servers residing on foreign soil, how could a globally distributed Blockchain work?
Suddenly this ICANN like body, becomes the gatekeeper of all global transactions and to function would required the buy in of almost all of the worlds economies.
The politics involved, in running this type of body beggars belief. An International Monetary Fund, in charge of a global unified digital currency. Some people's worse fear I suspect.
The opposite view, is that yes, global data laws are likely to crush the Blockchain for good.
