Anisole is methoxy benzene. Anisole reacts with protons from hydroiodic acid to form methyl(phenyl) oxonium ion.
In the methyl(phenyl)oxonium ion, the oxygen atom has a positive charge. This positive charge is delocalised through resonance with the benzene ring. Due to this, the bond between the oxygen atom and the aromatic carbon atom of benzene has a partial double bond character. This bond is difficult to break. Hence, the iodide ion does not attack the aromatic carbon atom of the benzene ring. On the other hand, the bond between the oxygen atom and the carbon atom of the methyl group is a single bond. This bond can be easily broken.
Hence, the iodide ion attacks the carbon atom of the methyl group to form phenol and iodomethane.