The p-values represent the likelihood of obtaining the observed results if no real difference existed, and various methods are available to calculate p-values.
The lower the p-value, the greater the statistical significance of the associated fold change values. The higher the p-value, the smaller the statistical significance of the associated fold change values. More extreme fold change values tend to have smaller p-values. More samples can improve p-values, especially for smaller changes in expression or smaller fold change values.
Calculating p-values is a bit complicated, and there are a number of methods to correct them for false discoveries. However, the RNA-seq Analysis Portal automatically calculates them for you and corrects for false discoveries, once you set up your RNA sequencing-based differential gene expression analysis by defining the samples and groups to be compared.