Can anyone tell me what this little white box on my outlet is?
Conveniently, it still had the UPC barcode label and you captured it quite clearly in the picture.

A search at upcdatabase.com shows that it is:

Description     Brinks Home Security System AC Power Adaptor
Size/Weight     5x3x3, 12 ounces 
Issuing Country United States


A Google Search for that UPC brings up a number of hits, including on at Parts Express that shows the following specs:

Universal UB1640W 16.5 VAC 40 VA Plug-In Wall Transformer

AC Output Voltage   16.5 V
Current Capacity    2400 mA
Center/Tip Polarity AC Plug 
Input Voltage       110~120 VAC




So, it appears to be a low voltage 16.5 VAC transformer that is (or at least was) a part of a home security system. Looks like the screw on top is meant to screw into the outlet for semi-permanent installation. 

Of course, it's possible that it was re-purposed for something else like low voltage lighting, a doorbell, or who knows what it may be used for.