This is an Encore ENRXWI-G "Wireless LAN Extender". I needed to extend my home Ethernet into the basement, for a project I'll describe later. For about $30 (newegg.com), this box saves me an hour or two struggling in my crawlspace for CAT 5 installation. That's a fair trade, I'd say! I bought two of them, with one as a spare.
In addition, it turns out this is a Linux box. (If you're up to it, you can reverse engineer the system and flash it with your own OS. But I will let that exciting project go for now...) And it can actually be used as a full-blown WiFi access point and in a couple of other modes. The only limitation is its single 10/100 baseT Ethernet connection.
I did try the "Repeater" mode with the second unit. Maybe this would help me get a better signal to the basement ENRXWI-G? My main WiFi access point happens to throw a shadow into the basement area that I am using, probably because of an intervening brick chimney. Moving my AP a foot or two seems to cure the problem, but could the repeater function do the same? I set it up according to instructions, and it seemed to help on the basement-to-AP route, but if anything hurt the performance (lost packets, etc) AP-to-basement. (puzzling) In any case, no joy.
A WiFi repeater is probably more appropriate when your client and AP are truly separated by long distances, and the signal strength directly from client to AP is really weak. The AP-to-basement path here is relatively short. My transmission errors may be due more to multipath reflections than to weak signals.
The only downside of this box, shared with most WiFi devices, is that there is a lot of setup required. The supplied documentation is about average, but many people will scratch their heads at some point when setting things up.
In summary, score one for cheap Internet appliances.