When the market changes its view of a company sufficiently to make calculation ratios such as PE substantially higher or lower, this a re-rating.
Price movements, particularly large ones can be looked at by being broken down into two components:
A share price goes up (or down) either because the profits (or cash flows) have increased (or decreased), or because the valuation multiples have become greater (or smaller).
As changes in profits and cash flows usually take longer to happen than changes in rating, correctly predicting how the rating will change will bring high returns.
This means that investors will usually do not only need to consider whether or not they believe a share is undervalued or over valued. They also need to consider what could act as a catalyst for re-rating. This is particularly true when looking at the short term.
Instead of profits the rating may be considered relative to any metric of value: sales, cashflow, NAV, etc. In practice the term re-rating is most commonly considered to have occurred because the PE has changed. However, as a re-rating implies a price change without a change in reported results, this almost always means that all valuation multiples have changed.
A re-rating may be specific to a particular security or issuer, or it may apply yo a whole class of securities. For example, shares may be re-rated. In the case of a general re-rating individual securities that follow their peers are not generally considered to have been re-rated.
The word de-rating needs to be used with a bit of care because it may mean a downward re-rating, but it may also mean a lowering of a credit rating or a reduction in some other kind of grading (such as the rather pointless fund ratings some research firms produce), to say nothing of a many more meanings outside investment.