out of 27464 with nonzero total read count adjusted p-value < 0.1 LFC > 0 (up) : 0, 0% LFC < 0 (down) : 0, 0% outliers  : 0, 0% low counts  : 0, 0% (mean count < 0)  see 'cooksCutoff' argument of ?results  see 'independentFiltering' argument of ?results
The p-value is the probability (hence "p"-value) of the obtaining this data or more extreme data assuming the null hypothesis is true. (definition of "more extreme" is dependent on the null and alternative hypotheses)
There is a tradeoff. When we try to be precise, the explanations become a little unwieldy and make the definition hard to remember. When we make the explanation simple, the wording is ambiguous.
Here is a definition that I like, tries to reconcile the two extremes:
The p-value is the probability that the observed difference between two groups is due to chance.