I had no idea this was a technique! From a British Antarctic Survey report on these devices[1]:
Accuracy
In field trials at Bird Island, South Georgia, the mean
error (great-circle distance) in position estimation
of static devices was 85 km, with standard deviations
in latitudinal and longitudinal errors of 0.61° and
0.99°, respectively (BAS, unpublished data).
I think they have a microprocessor, a battery, some sensors and flash memory. To get the data out you have to find/catch the swift and remove the device. The device wakes every 5 mins and records briefly.
Unit conversion: 0.04oz is approximately 1.14g, which sounds pretty impressive. But it can't be much heavier because a common swift typically only weighs around 35-56g (that's 1¼–2oz) according to http://www.commonswift.org/swift_english.html
According to the Wikipedia article linked by mongol, these devices can be as light as 0.3g. It's a battery, a phototube, a clock, and a recording chip. Longitude can be reconstructed from the time of most/least light, whereas the length of day and night allow reconstruction of latitude. Battery life is between 6 months and 5 years.
Love to study that - power source, communication methods, etc.