A reaction is stereospecific if reagents that differ only in stereoisomerism are preferentially or exclusively transformed into products that also differ only in their stereoisomerism. That is, the stereochemistry of the starting reagents determines the stereochemistry of the resulting products.
For example, the concerted addition of dibromocarbene (: CBr2) to the double bond, by one of the faces of the plane containing the alkene, leads in the cis-2-butene to the cyclopropane cis (the two methyl groups located in the same face), while the addition on trans-2-butene generates the racemic mixture of the trans product (each methyl group located on the opposite side of the cyclopropane).
Therefore, stereospecificity derives from the mechanism of the reaction. This means that the stereochemistry of the products is determined by the way the reaction takes place mechanistically.
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