Fitbits have 2 measurement modes for sleep - normal and sensitive. Normal pretty much tracks me as sleeping like the dead for 8 hours each night (however long I'm immobile in bed). Sensitive, on the other hand, tracks much more detail and can tell when I'm restless, sleeping deeply, and even when I get up in the night and move around. I highly recommend the sensitive sleep setting for Fitbit users - it gives you more data to play with!
Fitbit recently re-worked the way they track sleep in its HR-monitor-equipped devices (Charge 2, Aria HR, etc.). It introduced more details (it was just tracking restless/deep before) and this upgrade greatly improved the sleep tracking for me. Before Sleep Stages, it would track only 3-4 hours of my sleep each night. Now, it catches the full 6-9 hours.
Now, all of this is to be taken with a grain of salt in terms of accuracy, but to compare among Fitbit users and to yourself over time, this information is incredibly useful!
The strongest example of the usefulness of this for me so far has been the effect of moderate alcohol consumption on the quality of my sleep. I am far more restless and get much poorer sleep after drinking just 1-2 beers on a full stomach. This has led me to cut back almost completely on alcohol and the quality of my rest has dramatically improved!