1. become completely known, felt, or understood
let the good/bad news sink in
In a literal sense, if something was to 'sink in' to something, like water, it would be slowly absorbed by it. Figuratively, therefore, this expression relates to information or knowledge of some kind being absorbed or dealt with by a person over a period of time that can range from seconds to years, depending on how long it takes the brain to fully process it. This term is common in both a social and professional context, and is similar to the phrase 'get through to someone.'