bitterchocolate said:

How and why does a one-tailed compared to a two-tailed test one affect the ability to identify significant differences?

In a two-tailed test, the alpha-risk (Type I error), or the chance that your assertion of a significant difference is incorrect, is divided between the two tails, and requires a larger test statistic for a significant result.

Let's say you need to do a two-tailed t-test, and you set alpha = .05. That alpha gets divided by the two tails, so you end up with .025 in each tail. In order to get a significant t-statistic, it would need to be larger than if you did a one-tailed test where all of the .05 alpha risk is in one side.