Anonymity problem
Government and government agencies have always spied their people. In past decades they started spying people’s Internet activity also. The awareness was brought to masses when Edward Snowden, an ex NSA employer, explained that all our Internet activity was spied by NSA. This also applies to people that are not living in the USA, since most of the servers are located in the USA.
A solution needed to be developed, that is why TOR project was developed. The TOR is using Onion protocol which basically encrypts your traffic, making multiple layers of encryption around it (onion analogy), then it sends your traffic to different nodes (onion routers) and decrypts each layer in a single node, which shows only where the traffic needs to be sent next. The reason why this is so secure is that no info rather than this is shown in a single node. The exit node is the last node in the line and there your traffic reaches its final destination. 
The problem with TOR
Some governments are restricting access to the TOR network. They are using deep package inspector to analyze the data of your Internet connection, and if they detect that you are using ONION protocol, they will restrict that connection. Some of the countries that have blocked or are trying to block TOR are China, Saudi Arabia, Iran, and France. Governments of the world are trying to block TOR to forbid anonymity on the internet, and there will be more countries that forbid using TOR. For those who live in those countries, the only way to use TOR and its benefits is to somehow “mask” that they are using TOR.
There is a solution for accessing. The countries can access the TOR by creating network tunnels, like VPN, to reach to the country where the TOR is not banned. The problem with that approach is that the connection between the user and the country that the one is trying to connect to is not encrypted, which means ISP, government and others can inspect the data. This is where obfuscation comes to the scene. 
Importance of OBSF4
The solution for the mentioned problem is to use some kind of obfuscation. There are many obfuscation techniques, but the latest and the most secure is obsf4. Obsf4 is obfuscating or encrypting the data between the user and the TOR node, making it impossible for the Man-in-the-middle to analyze the packets and detecting that the TOR is used. Here the author explains in detail what is obsf4:
This is a protocol obfuscation layer for TCP protocols. Its purpose is to keep the third party from telling what protocol is in use based on message contents.
Unlike obfs3, obfs4 attempts to provide authentication and data integrity, though it is still designed primarily around providing a layer of obfuscation for an existing authenticated protocol like SSH or TLS.
Like obfs3 and ScrambleSuit, the protocol has 2 phases: in the first phase both parties establish keys. In the second, the parties exchange super-enciphered traffic.
For more information about the obsf4, read here https://github.com/Yawning/obfs4/blob/master/doc/obfs4-spec.txt
Why is this important for a cryptocurrency
More and more countries are banning cryptocurrencies because they are slightly inconvenient for them because they are not controlling it any way. For almost a century, governments are printing money without backing. Before there were backed by gold, but now, there isn't anything to back the printed money. Bitcoin was the pioneer of decentralized currency, with PoW to back it up. The problem that Bitcoin has is that it isn't anonymous. A lot of altcoins are trying to be anonymous, but very few are fully TOR integrated. DeepOnion is one of the currencies that is completely TOR intregrated and, on top of that, it is now enpowered with obsf4, to make your transactions as private as they can be. This is why the future of cryptocurrencies lies in coins like DeepOnion. Check it for yourself on https://deeponion.org/.
