Why is phenol acidic?

Compounds like alcohols and phenol which contain an -OH group attached to a hydrocarbon are very weak acids.

 Alcohols are so weakly acidic that, for normal lab purposes, their acidity can be virtually ignored.

 However, phenol is sufficiently acidic for it to have recognizably acidic properties - even if it is still a very weak acid.

 A hydrogen ion can break away from the -OH group and transfer to a base.
For example, in solution in water:

Phenol is a very weak acid and the position of equilibrium lies well to the left. Phenol can lose a hydrogen ion because the phenoxide ion formed is stabilised to some extent. 

The negative charge on the oxygen atom is delocalised around the ring. The more stable the ion is, the more likely it is to form. 

One of the lone pairs on the oxygen atom overlaps with the delocalised electrons on the benzene ring.

This overlap leads to a delocalization which extends from the ring out over the oxygen atom. 

As a result, the negative charge is no longer entirely localized on the oxygen, but is spread out around the whole ion.

Spreading the charge around makes the ion more stable than it would be if all the charge remained on the oxygen. 

However, oxygen is the most electronegative element in the ion and the delocalized electrons will be drawn towards it. 

That means that there will still be a lot of charge around the oxygen which will tend to attract the hydrogen ion back again. 

That is why phenol is only a very weak acid.
Why is phenol a much stronger acid than cyclohexanol? To answer this question we must evaluate the manner in which an oxygen substituent interacts with the benzene ring. 

 It was proposed that resonance delocalization of an oxygen non-bonded electron pair into the pi-electron system of the aromatic ring was responsible for this substituent effect. A similar set of resonance structures for the phenolate anion conjugate base appears below the phenol structures.