Segmented sleep is a term used by historian A. Roger Ekirch to refer to a specific sleep pattern that he found when studying the nighttime habits of Europeans in the centuries from 1500 to 1700. He found that written accounts of the time referred to a 'first sleep' and a 'second' or 'morning sleep', with a period of 'watch' between. These terms and their equivalents were used in English, French, Italian, and other languages, with identical meanings. Romans apparently also used these distinctions.
People of this time period would come home exhausted from a long day's work, eat dinner, and go to bed. After a period of deep sleep, they would wake up around midnight, and spend an hour or two in relaxed activities. These activities included chatting, thinking quietly, sex, writing (if literate), or simply drifting in a semiconscious state. One might leave bed to do some light work, smoke a pipe, or talk with a neighbor.
This gives an interesting aspect to the idea of the witching hour. It may not have been a time when all were asleep and witches snuck around unnoticed. Instead, it was a time when everyone was awake, and aware to the odd sounds and shadows in the night. A mini-Halloween every day.
A study at the National Institute of Mental Health found that modern Americans, when asked to sleep for 14 hours a night, started sleeping in much the same pattern. They would lay awake for a few hours before falling asleep, sleep for three to five hours, and wake back up. After about an hour or so of quiet wakefulness, they would fall back asleep until morning. This puts insomnia in an interesting light; next time you have trouble getting to sleep, you might try just laying back and enjoying it.
Many people take these studies as a sign that this sleep pattern is 'natural', and that we would all be happier if we all slept like this. Similar sleep patterns have been reported in other 'primitive' cultures, and modern (often unrestful) sleep patterns are often blamed on the effects of artificial light and the pressure that modern society puts on us to spend only eight or less hours in bed.
Probably this has some truth to it, but I am a skeptic. This skepticism is primarily based on personal experience; I spent two years with no artificial lights (except for candles), and little pressure to keep to any particular sleep schedule. I did not take any sleep aides, I did not set alarm clocks, and I did not fall into a pattern of segmented sleep. While one anecdote does not a theory break, I am far from convinced of the 'naturalness' of segmented sleep. I suspect that it just one of many sleep customs that have appeared in human cultures, no different in spiritual significance than siestas or sleeping in on the weekend.
"Let the end of thy first sleep raise thee from thy repose: then hath the body the best temper; then hath thy soul the least encumbrance."
-- Francis Quarles, 1592-1644
A. Roger Ekirch (2005), At Day's Close: Night In Times Past. ISBN 0-393-05089-0 (Included for completeness, although I have not yet found a copy to read myself)