There are several ways to help make a coin private, and one of those is for it to run over the "Tor" network.
What is the Tor network, is a question that is often asked by people new to the world of privacy coins. It is short for "The Onion Router" which I can presume is how DeepOnion recieved its name. Initially created by the U.S Navy it is now a not for profit organisation helping to make privacy more accessable for people around the world.
What this router does is as follows:
The Tor network disguises your identity by moving your traffic across different Tor servers, and encrypting that traffic so it isn't traced back to you. Anyone who tries would see traffic coming from random nodes on the Tor network, rather than your computer.
In the example of DeepOnion, when you connect to the Onion network you are connected to one of the many Tor Servers, so that your transactions are not traced back to you.
Currently if people know your Onion wallet, they can still trace these transactions using the block chain explorers, however I will come onto that with a future post about the DeepSend project that is in the works and how this will help to eliminate this problem.