The similarity just lies in the structure. DNA is double-stranded, however it is twisted/helical, while the ladder does not twist. However, other than that, they are quite similar. The 2 strands (5' -> 3' and 3' -> 5') of DNA serve as the 2 vertical sides of the ladder. The base pairs of DNA are what connect the two strands together. So, in terms of the ladder, think of the steps of the ladder as the base pairs. Think each step as consisting of 2 entities joining together to make 1 big step. For example, think of a step having 2 halves down the middle. 1 half would be a guanine (base) and the other half would be a cytosine (base). Guanine is connected to the 5' --> 3' strand (Left vertical side of ladder) while the Cytosine is connected to the 3' --> 5' strand (right vertical side of ladder). These two come together at one of their ends and base pair, which appears to look like the steps on a ladder.
