In resonance structures, the chemical connectivity in the molecule is same but the distribution of electrons are different around the structure. They are created by moving electrons in double or triple bonds, and not atoms.
Phenol, [tex]C_6H_5OH[/tex] and methanol, [tex]CH_3OH[/tex] both are alcohols that contain an [tex]-OH[/tex] group attached to carbon atom.
Due to loss of 1 [tex]H[/tex] from phenol, it forms phenoxide anion and due to presence of double bond in the benzene ring the negative charge on the oxygen atom (which represents electrons) will resonate with double bonds of benzene ring as shown in the image. The resonance-stabilized phenoxide ion is more stable. Whereas when methanol lose 1 [tex]H[/tex] it forms methoxide anion and there are no such electrons present in the structure of methoxide that will result in the movement of electron. Since, due to resonance-stabilized phenoxide ion is more stable than methoxide ion, so it is a stronger acid.
The structures of the anions resulting from loss of 1 [tex]H[/tex] from phenol and methanol is shown in the image.