Instead of chosing a static route ahead of time, ExOR defers the choice of the next forwarding node until the reception of the packet which is to be routed. The forwarding is done by the node closest to the destination, so the route is built dynamically. Using a mechanism of acknowledgements (ACKs), we can ensure, that only one node forwards the packet.
Let's look at an example transmission, taking place in the network represented by the following figure, where the edges are labeled with the delivery ratios (= probability of reception):
Assume, we want to send a packet from node A to node D. One extreme would be to send the packet directly - at the expense of sending it multiple times because of likely losses. The other extreme is a 3-hop route through B and C - at the expense of sending the packet 3 times. Imagine you are sitting in a crowded pub and want to pass a message to a friend on the other side of the room. You could tell it someone directly sitting next to you, but it will take a long time until it reaches your friend (apart from some serious Chinese whispers effects, which - I admit - are unlikely in computer networks ... Hmm, maybe we should do some research related to this ... could be fun!). Another possibility would be to shout your message loudly into the pub, but you surely would have to do this multiple times, until your friend hears it.
Both strategies leave some performance on the table, so ExOR tries to send the packet as far as possible by selecting the node as the forwarding node, which has the least remaining distance to the final destination. (Imagine you shout the message for your friend loudly into the room - and we elect the person as the forwarder, who is nearest located to your friend among all persons who successfully heard what you said.)