Sentence:  The most important property of the <WSD>Kronecker delta</WSD> occurs when it shares a common repeated index with another tensor: / Note 10.1.3. "When an index of a tensor T is contracted with one of the indices of the <WSD>Kronecker delta</WSD>, the result is an expression in which the <WSD>Kronecker delta</WSD> is removed and the contracted index of T is replaced by the other index of the <WSD>Kronecker delta</WSD>." 
Meaning of the word marked with <WSD> tags:  A binary function, written as &delta; with two subscripts, which evaluates to 1 when its arguments are equal, and 0 otherwise.