Acidity of phenol and aminophenol?

Phenol is more acid than 4-aminophenol.

Phenol as an acid: C₆H₅-OH ⇌ C₆H₅-O⁻ + H⁺
4-nitrophenol as an acid: H₂N-C₆H₄-OH ⇌ H₂N-C₆H₄-O⁻ + H⁺

Amino group (-NH₂) is strong electron releasing (electron donating) by resonance effect, although nitrogen is a very electronegative element. The effect of electron releasing of amino group would destabilized the H₂N-C₆H₄-O⁻ ion as the negative charge is more concentrated at the oxide ion. Therefore, considering the backward reactions, H₂N-C₆H₄-O⁻ ion would be protonated more readily than C₆H₅-O⁻. In other words, C₆H₅-OH would donate proton more readily than H₂N-C₆H₄-OH, and thus C₆H₅-OH is a stronger acid than H₂N-C₆H₄-OH.

The NH2 group feeds electrons into the ring (it's a powerful activating group). This will strengthen the O-H bond weakening the acidity.

phenol has a pKa of 9.95 in water
4-Aminophenol has a pKa of 10.30

phenol is more acidic