To 'sink in' means to 'be absorbed'. If something has sunk into something, it has been absorbed. We can use this phrasal verb literally, as in water sinking into the ground. Or, as in this case, we can use it figuratively to mean that a person has taken in, or 'absorbed' some information.

sunk is the participle form of the verb to sink (тонуть). "To sink in" means to understand or comprehend something (information or feelings). What there're saying is you should turn the page(?) over once you understand the information that's there.