Two sequences can be aligned in such a way that the identical residues will be on top of each other. Unfortunately, there are many ways to align two sequences. Consider the two words: WORD and BIRD. We intuitively feel that the best alignment is

      B I R D
          | |
      W O R D

Aligning WORD with BEARD is more difficult, we have a number of similar solutions like:

    B E A R D    B E A R D    B E A R D
          | |          | |          | |
      W O R D    W . O R D    W O . R D

In mathematical terms, we can use the unit operations of insertion, deletion and replacement to edit a word. After a number of such unit operations we can transform WORD to BEARD. The minimum number of operations is the so-called Levenstein distance of two words. In sequence alignment we operate with a specific weighted version of this distance concept: We assign specific weights to insertion, deletion and replacement, as described in detail under Database searching. Specifically, the replacement matrix most often used is the Dayhoff matrix, that represents the evolutionary weight of amino acid replacements. In protein comparisons we often use the BLOSUM matrix, which is specifically designed for database searches.

Suffice to say for now that we have a distance function which will be zero for identical sequences. Or, what is essentially the same, we can use the similarity score, which is maximal for identical sequences.