Assertion (A) is True. The acidity of a compound depends on its ability to lose a proton ($\mathit{H}+$) and the stability of the resulting anion. p-nitrophenol is significantly more acidic than phenol (the $\mathit{p}{\mathit{K}}_{\mathit{a}}$ of p-nitrophenol is ~7.1, while phenol is ~10).
Reason (R) is True. The nitro group ($-\mathit{N}{\mathit{O}}_2$) is a powerful electron-withdrawing group. It exerts both a strong inductive effect (-I) and a strong resonance effect (-R).
When p-nitrophenol loses a proton, it forms the p-nitrophenoxide ion. The nitro group at the para position helps delocalize (spread out) the negative charge from the oxygen atom into the nitro group itself. This "dispersal of charge" makes the phenoxide ion much more stable.
Why (R) is the Correct Explanation for (A)
In organic chemistry, the more stable the conjugate base (the phenoxide ion), the more acidic the parent acid. Since the Reason (R) correctly identifies that the nitro group stabilizes the conjugate base through electron withdrawal, it explains why p-nitrophenol is more acidic than plain phenol, which lacks such stabilizing groups.