Definition of doublette
A doublet is when a board is paired. For example, if a board is 2-5-6-7 and the river brings a 2, we would say that there is a doublet since the board "pairs" (there is a pair on the board). The reason for counting pairs is that on a board with a pair, there is now a possibility of a full hand. Just as you have to watch out for a third spade on the river when you have a straight (your opponent could have a flush), you have to watch out for a doubleton when you have a flush. (our opponent could have a full hand).
Hold'em and Omaha Doublettes
A double up changes the dynamics of a table, but in Omaha, much more than in Hold'em. Full hands in Omaha will be at least twice as common as in Hold'em. Some pairings are more important to watch than others. For example, if we go back to our chart above, in Hold'em, our opponent will rarely have a 2-of-a-kind and probably a full hand with only 88 and 99. Few players play 42 or 92. On the other hand, on an A-K-J-Q-A board, the ace will be a more worrisome double up if you have a flush or straight since AK, AQ and AJ are hands that your opponent is more likely to have than a 4-2 as above.