Sleep Tracking:
The Jawbone UP3 does it by monitoring a user's bpm (heart rate beats per minute), respiration rate, body temperature and galvanic skin response, it can give you your REM, light and deep sleep stats.
See UP3: The world's most advanced tracker - The Jawbone Blog

The bioimpedance sensor in UP3 can look deeper inside the body, and is tuned to look for signals at specific depths. The sensor measures very tiny impedance changes within your body. For heart rate, we are measuring the impedance changes created by the volume of blood that is flowing in the Ulnar and Radial arteries. Because we are able to see the arterial flow, we believe it can maintain a more accurate tracking of your heart rate at your wrist than traditional sensing systems.

Further, because we can control how deep the sensors penetrate we can extract many other signals beyond heart rate. We will be able to see respiration (largely due to changes in oxygen in blood and surrounding cells) and hydration.

Problem with light sensor for heart rate:
There are well-reported issues with skin tone and light interference, but more importantly, optical sensors measure your heart rate by looking at blood flow through your capillaries. While this is a good measure at low heart rates, the blood flow slows as it moves from the arteries through the capillaries below the skin making it imprecise. Source: The Jawbone Blog

At "Personal Sleep Monitors: Do They Work? | Huffington Post",
Dr. Christopher Winter, Medical Director, Charlottesville Neurology & Sleep Medicine, sleep medicine, neurology specialist, says,
"The simple theory is movement equals wakefulness and prolonged lack of movement equals sleep. This technology, known as actigraphy, has been around for decades and is a useful tool for mapping general patterns of sleep. While some companies claim that they can provide detailed sleep quality measures with actigraphy, to do so would be the equivalent of determining how well a car is driving by its odometer reading alone."

"To put these devices to the test, I needed a gold-standard evaluation of my sleep quality. To achieve that, I underwent a true sleep study. This combination of brain wave tracings, muscle-tone evaluation and eye-movement analysis, along with a live audio/video of my sleep allowed me to see exactly what was happening during my slumber."

Dr. Winter translated the output of all of the devices into a common visual reference to allow for easier comparison.

search?q=how+does+motionx+activity+tracking+work
94% represents the amount of sleep, 7:31, as a percent of my goal, 8hrs.

Software:
MotionX^® | MotionX-24/7 Overview

Links:
Best Fitness Tracker | Activity Monitor Review - Consumer Reports
The Best Fitness Trackers for 2016 | PCMag.com
Best fitness trackers 2016: Jawbone, Misfit, Fitbit, Garmin and more | wareable.com
The Best Fitness Trackers | The Wirecutter Tests accuracy
Personal Sleep Monitors: Do They Work? | Huffington Post

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