As the name implies, a bridge connects your local network, to the ISP.. the ISP network may comprise many other DSL subscribers. A bridge has little built-in intelligence, it passes all data it sees on one side of the bridge, to the other side, no matter whether that is the correct destination for the data or not.
Bridged networks are simple to setup when small, but with more and more subscribers, they can start to waste bandwidth with "noise": packets of data that are not meant for you.
Noise on a bridged network should not be confused with the traffic on a shared ethernet, on a bridge, only certain categories of data (broadcasts and ARPs) are passed to network nodes by the bridges, nevertheless, as the size of the bridged network increases, broadcast traffic can rise to be a significant fraction of the link bandwidth. Network configuration problems can also give rise to "storms" where links are flooded with packets making communication difficult.
Routed DSL places a router at your end, and the router "knows" about your network, and also knows about the router at the other end (at the ISP), meaning that it passes traffic that is yours, and destined for the internet, over your link.
Routed DSL, if available, is a more expensive option than bridged DSL, and is normally only provided in a business DSL package. Business DSL packages have higher quality of service guarantees, and these can be better met with routed DSL. Routed DSL is also slightly more secure, as it is harder for intruders who are on a nearby address to impersonate machines or snoop traffic.

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