The simple version: Tor provides a distributed network of servers ("onion
routers"). Users bounce their TCP streams (web traffic, FTP, SSH, etc.) around
the routers. This makes it hard for recipients, observers, and even the onion
routers themselves to track the source of the stream.

The complex version:  Onion Routing is a connection-oriented anonymizing
communication service. Users choose a source-routed path through a set of
nodes, and negotiate a "virtual circuit" through the network, in which each
node knows its predecessor and successor, but no others. Traffic flowing down
the circuit is unwrapped by a symmetric key at each node, which reveals the
downstream node.