Sleep is a measurement of the raw time you've spent awake: the longer you are awake, the higher your Sleep value is.
Beverages containing a bit of caffeine will reduce this value, as will stopping your adventure and taking a nap. Furthermore, sleeping in a bed you own or have rented will get you the Well Rested bonus for 12 hours.
As your sleep deprivation worsens, your Agility and other stats will be affected. Not sleeping for two weeks will cause you to die.
Well Rested bonus when you sleep outside, even in a unowned bed
pcps3xbox360 Sometimes the SLP meter in your Pip-Boy 3000 can get stuck on zero, and in fact will not display any number below the indication arrow. During this time your character will not advance in sleep deprivation. This bug may be fixed by finding a bed and sleeping for any amount of time. After the player wakes, the gauge will begin displaying a number again and will increase over time normally.