Hi, ori. I haven't been around much, but it's good to see you still posting.
The p-value is a statistical term that means the likelihood of that observation occurring by chance if there are no actual differences. The assessment against "no actual difference" is called the null hypothesis and scientists usually hope to reject that hypothesis. Most studies are set to reject the null hypothesis if the p-value is less than 0.05. In this case the p-value of <0.001 means that the null hypothesis is rejected and significant differences have been found.
What your statement doesn't go into is the concept of the power of the study. Generally, the higher the number of participants in the sample, the higher the power of the analysis and the narrower the gap between the differences is to find significance. In this case 56.6% was found to be strongly significantly different than 52.3% (p-value much lower than 0.05). In another study with a smaller sample size and less power the p-value may have been closer to 0.05, or even above it, resulting in no significant differences observed. The absolute numbers don't tell you much. Keep in mind that these are samples of a population, not the entire population, and the gap between differences become significant based on more than just the absolute numbers.