As you point out, DNA is a double strand. The four bases (adenine, thymine, cytosine, and guanine) that bond and connect the two strands can only bond in the specific pairings of adenine with thymine, and cytosine with guanine. Because of this, each individual strand forms a template, or a sort of chemical mirror image, of the other strand.
Therefore, if one strand is damaged the remaining intact strand can be "read " by the cell to see what the base sequence needs to be in the strand that is being repaired. So having a double strand makes DNA repair much more likely to be done correctly.