Currency correlation tells you if the two currency pairs are moving in same direction or opposite direction and how strong is that the correlation between those pairs. If two pairs move in the same direction very strongly then you should be avoiding taking a long (buy) position for one pair and simultaneously short (selling) position for the other pair and vice versa. This is the first use. -
currency pairs ?...or individual currencies ? - big big difference
Second use is that it is possible that the long term average correlation is quite strong. For example 2 pairs generally move in the same direction quite strongly. At times you may notice that suddenly that correlation has changed drastically. May be one pair is moving up very fast but not the second. Considering the longer term history you may like to buy the second pair because it may catch up with the first or the opposite i.e. short-sell the first.
..........again pairs or individual currencies ?