AirPort Express can function as a full-fledged wireless access point, or it can join an existing network just to offer its wireless print server and audio features. When AirPort Express does that, it is in "client mode."
In client mode, AirPort Express does not offer itself as a wireless access point or use its Ethernet port. As a wireless client, AirPort Express is simply a destination for AirTunes and print jobs. It can join both 802.11b and 802.11g networks, including those using security features such as WEP and WPA-PSK.
In client mode, the ProxySTA feature allows wired clients to be connected via Ethernet (with 802.11n-based AirPort Express only).
Wireless Distribution System is another way for AirPort Express to join an existing Wi-Fi network. AirPort Express uses its Ethernet port and can offer its wireless access point in WDS mode, but it requires that your other access points be AirPort Extreme and/or AirPort Express. Client mode's advantage is that you can join the networks of non-Apple access points and earlier AirPort base stations ("Dual Ethernet" and "Graphite" models).
Other Wi-Fi product manufacturers have different names for "client mode." These include "client station mode," "AP client mode," "wireless client mode," and "STA mode." Whenever one of these modes is required, just remember that "client mode" is the same thing.