On the first step, the oxime oxygen gets protonated and acquires positive charge.
On the rate-limiting second step, the positively charged oxygen pulls an electron pair from its bond with nitrogen, breaking this bond, and releasing a molecule of water. At the same time, nitrogen pulls an electron pair from the bond between the C=N group and the anti-substituent (R1), shifting the bond with R1 bond from carbon to nitrogen, and generating positive charge on that carbon.
On the third step, the positively charged carbon accepts an electron pair from a molecule of water, shifting the positive charge to oxygen.
On the fith step, the protonated oxygen protonates nitrogen, which pulls an electron pair from the C=N bond, converting it to a C-N bond, and shifting the positive charge to carbon.
On the sixth step, the positively charged carbon pulls an electron pair from the adjecent O-H bond, reinstates the carbonyl group, and releases a proton to the solvent.