Palimpsest comes to us from ancient Greek, meaning scraped again. Many of the earliest books were written using pages made from animal skin (known as parchment). The skin was prepared by first being scraped free of hair, then stretched and treated to make it into a remarkably resilient material. Parchment was very expensive, and, for much of human history, the physical materials that comprised books were often considered more valuable than the texts they contained. As such, it was a relatively common practice to scrape the parchment again (often in combination with an acid treatment or similar technique) to erase an extant text so that the materials could be reused.
Fortunately for us, the ink used in many of these books was highly acidic as well, making the original texts relatively durable. Significant scholarship has gone into recovering these palimpsested texts, and many incredible discoveries have been made as a result. A previously unknown work of Archimedes was recovered from one such palimpsest, showing that the great inventor fathered mathematical disciplines such as Combinatrics. You can see that recovery project here.
In my seminal paper on the topic, Preparing for the Age of the Digital Palimpsest, I recontextualize palimpsesting as a modern phenomena, involving data that has been deleted or partially overwritten on digital media. In much the same fashion as evidenced in ancient and medieval palimpsests, the storage media is seen as more valuable than the data preserved on it. In many cases this will be an accurate assessment, but not in every case. We have already seen evidence of this, in situations such as the lost moon landing tapes.
Because we can't save everything, inevitably we will regret some of our preservation choices. Information Science, as a discipline, must be prepared to assist in Digital Palimpsest Recovery efforts, using tools developed by fields such as Digital Forensics . . . tools which Information Science will hopefully have a hand in improving.
It would be a mistake to embark on such recovery efforts with the goal of recovering data. Instead, the Literary Studies view of what constitutes a text should guide such efforts. Recovering a text is a very different project than recovering data (think of the difference between recovering 60% of a year's census data as opposed to recovering 60% of Macbeth). This conceptualization gives us different goals, but also provides us with different tools to recover missing data through semantic and linguistic evaluation.
We must also not forget the hard-learned lessons from Manuscript Studies. We must preserve context and use only non-destructive modes of recovery, to name only two important things the work on physical manuscripts can teach us.