A reverse is a rebid in a suit which is higher ranking than the original bid at a higher level without jumping. This can be either opening a lower suit and then rebidding a higher suit immediately after, or else responding and then rebidding a higher suit.
In the following bidding, opener is said to have reversed by bidding 2♥:
If the rebid is at the 3-level without jumping, it is called a high-level reverse, as follows:
It shows even more strength than a standard reverse, and is game forcing.
Reverses tend to show more points than a simple new suit, but not (necessarily) as much as a strong jump shift might, particularly after a 1/1 response, where partner has only shown 6 points. After 2/1, it is a less important distinction, and reverses are sometimes permitted (although not advised) even with a minimum opening, especially when the 2/1 response is game forcing.
This has an effect on which suit one should open. Therefore, when holding two consecutive suits of equal length, the higher should be opened first, in order to bid the second without a reverse.
A common objection to the normal treatment of reverses is that it prevents one from having a chance to show a four-card major. This is not the case, however. If partner skipped a major suit in his response, it is likely he does not have a four-card major, so there is no fit anyway.