When an idea or thought "sinks in", it means that you notice or realize it. For example:
This isn't something you can just cram for the night before. It takes at least a few days to sink in.
The true meaning of what the Reverend was telling us finally sunk in.
No rush. Take some time, let it sink in, and get back to me with an answer tomorrow.
"Sinking in" is a deeper experience than just "knowing". In the example above, the speaker knows that she's married, but it hasn't "sunk in" yet. She's waiting to not only know that she's married, but also to feel married.