A scoring function that assigns costs to edit operations inferred from an alignment. The simplest form of alignment score is the function associated with edit distance, in which the substitution, insertion, or deletion of any symbol is assessed a penalty of 1 (i.e., 1 is subtracted from the ongoing score).
The cost function is allowed to vary depending on the specific type of operation and symbol(s) used. We may even assign positive scores to matching symbols of the alignment.
When aligning two genetic strings, we desire to take the minimum alignment score (w/r/t our particular choice of scoring function) over all possible alignments of the two strings. This minimum score will offer us a quantitative notion of how much the strings have been separated by evolution, and an alignment corresponding to this minimum score will provide us with one possible collection of mutations that would have transformed one string into the other.