Tor (The Onion Router) is a network of proxies trying to protect your privacy. On Android this is usually implemented with Orbot and used with Orweb & Gibberbot.
What is TOR?
In short: A network of proxies to protect your privacy by adding a level of anonymity. Quoting Wikipedia:
Tor is a system intended to enable online anonymity. Tor client software directs internet traffic through a worldwide volunteer network of servers to conceal a user's location or usage from anyone conducting network surveillance or traffic analysis.
TOR logo (Source: Wikipedia)
The onion is part of the name, and part of the logo. Its several shells symbolize the several levels of nodes used to protect your connections: if an "intruder" manages to crack one, there's the next. A common TOR connection uses at least 3 nodes: an entry node (where you connect to), and exit node (connecting to your target), and one in between. Each one only gets the minimal information necessary, so e.g. the exit node does know nothing about you except your wish to connect to the target and the data to exchange with it.
How TOR works (Source: Wikipedia)
TOR for Android?
Yepp, available. There's Orbot: Tor on Android. And there are special bundles like Orweb: Proxy+Privacy Browser, Gibberbot: Secure Messaging, and the ND Private Browser -- all of them using the TOR network.
- proxy: There are several types of proxies available, which not necessarily offer anonymity (at least not in the sense of TOR).