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Concordance, as used in genetics, usually means the presence of the same trait in both members of a pair of twins. However, the strict definition is the probability that a pair of individuals will both have a certain characteristic, given that one of the pair has the characteristic. For example, twins are concordant when both have or both lack a given trait. The ideal example of concordance is that of identical twins.
Discordance, in genetics typically means that a similar trait is not shared between twin members. Studies of twins have shown that genetic traits of monozygotic twins are fully concordant whereas in dizygotic twins, half of genetic traits are concordant, while the other half are discordant. Discordant rates that are higher than concordant rates express the influence of the environment on twin traits.