Wireless Bridging is used to connect two LAN segments via a wireless link. The two segments will be in the same subnet and look like two Ethernet switches connected by a cable to all computers on the subnet. Since the computers are on the same subnet, broadcasts will reach all machines, allowing DHCP clients in one segment to get their addresses from a DHCP server in a different segment. You could use a Wireless Bridge to transparently connect computer(s) in one room to computer(s) in a different room when you could not, or did not want to run an Ethernet cable between the rooms. Contrast this with Client Mode Wireless, where the local wireless device running DD-WRT connects to the remote router as a client, creating two separate subnets. Since the computers within the different subnets cannot see each other directly, this requires the enabling of NAT between the wireless and the wired ports, and setting up port forwarding for the computers behind the local wireless device. Segments connected via Client Mode Wireless cannot share a DHCP server.
In the case in which we are interested, a wireless device running DD-WRT such as a WRT54G is configured as a Wireless Bridge between a remote wireless router (of any make/brand) and the Ethernet ports on the WRT54G.