The fitbit decides whether you are "sleeping" by how much your body is moving, and your heart rate. If you are essentially stationary and your heart rate has dropped below resting (seated and quiet for a time) heart rate for a certain amount of time, it'll read that as "sleeping".
Likewise, the brief periods of "awake" it registers during the night are where you're tossing and turning. You won't necessarily be conscious and responsive, able to have conversations, etc.
Tightness of the band influences measured heart rate; a slack band misses some beats and measures heart rate as lower, a tight one the reverse. The thickness of your wrist will vary through the day, for example you may set it loose, go for a walk on a warm day, and the warmth and the gravity pulling your blood into your hands as you walk will make your wrists swell slightly, thus it may read a wrongly-low heart rate when you start walking, and a wrongly-high heart rate towards the end.
It will register "light", "deep" etc sleep by your movement and heart rate, and so things like your hands being outside or inside the covers and thus more or less swollen, these will influence how it interprets your sleep.
Of course, there are factors other than the amount of "deep" sleep and the total sleep you have which influence how you feel the next day. If you didn't drink anything after dinner and it's a hot night, you may have a lot of deep sleep but be dehydrated on waking (sleep is commonly an 8 hour period without water), and so feel awful. But maybe mid-afternoon you're just a bit weary, have a twenty minute nap - far too short for "deep" sleep - and then feel great.
Fitbit, then, provides these numbers which purport to be both accurate and precise, but which really are just a rough sketch. What they're useful for is trends. It's like if you want to gain or lose weight - your weight will vary naturally day-to-day, and simply going to the toilet or eating a meal can be the difference of 0.5-1kg. So for weight gain or loss you look at the trend over weeks or months.
And then there's cardiovascular fitness. If you go for a hard run today, your resting heart rate tomorrow will probably be higher than it was today - you've stressed your body and it's now working hard to recover. But the day after that you go for another run anyway, and so on. Bad sleep makes it go up, as does worry about work, etc. Maybe it drops on weekends and when you spend time with good friends. So it's up and down day-to-day. But over weeks or months your resting heart rate trends downwards.
Likewise the data Fitbit offers you. Look at the data, and look for patterns. You keep doing X, and Y happens. You stop doing X, and Z happens. Depending whether you liked Y or Z result, you decide whether or not to keep doing X.
That's for things like heart rate and sleep. There are other things like the oxygen saturation and heart rate variability which are complete fiction. Ignore them. Basically all the premium data - the workouts are good, but the data are fiction.
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