The ITU-T E-model
In traditional telephony, voice quality has long been expressed by a metric called the Mean Opinion Score (MOS). Perception of audio quality is inherently subjective; different ears have different sensitivities, and people have varying expectations for what is acceptable, to point out just two variables. The MOS is determined by having actual people rate the quality of test sentences (read by both male and female voices) from 1 (poor) to 5 (Excellent), and calculating the mathematical mean.
For most deployments of VoIP, such testing is simply not practical. Even if you could get a large enough sample of users to come up with a meaningful number, in most cases you are more interested in predicting whether your network can keep voice quality within acceptable limits rather than verifying what users already know. This is why the International Telecommunications Union's Telephony group (ITU-T) has come up with the E-model (ITU-T Recommendation G.107).
The E-model uses cumulative measurements of objective impairments to estimate what their effect would be on users' perception of quality. In its simplest form, the E-model subtracts the impairments from the R-factor to come up with a score of 0 to 100:
R = Ro - Is - Id - Ie + A
Where Ro is the undistorted original signal (a constant of 100), Is measures the distortion of the speech signal from the telephone hardware, Id measures network delay and jitter, Ie measures the signal degradation due to speech encoding. A adds the users' typical expectations for the type of connection being used, accounting for the fact that people are willing to accept lower voice quality in exchange for some other benefit, such as the cost savings of DSL, or the mobility of wireless.
Observer implements the E-model to determine the R-factor, and thus calculate an estimated MOS score. It does this by constantly monitoring Id and updating quality scores per call and in aggregate. You can even set up an alarm to trigger whenever MOS scores (individually or on average) fall below acceptable limits.