seep
To slowly leak or spread through small openings.
When water or another liquid seeps through something, it moves slowly through small openings or pores, like how water gradually soaks through a paper towel or how melted ice cream seeps through a waffle cone. Seeping happens so slowly you might not notice it at first, but eventually you'll see a puddle, a stain, or a wet spot.
Rainwater seeps into the ground through tiny spaces between soil particles. If your roof has a leak, water might seep through the ceiling and eventually drip down. A wet sponge left on a countertop will seep water onto the surface beneath it.
The word can also describe how things other than liquids gradually spread or penetrate. Secrets sometimes seep out despite everyone's best efforts to keep them hidden. Cold air might seep under a door on a winter night. When you're camping and the morning chill seeps into your sleeping bag, you feel it slowly working its way through the fabric.
Seepage is the noun form, describing the slow movement itself or the liquid that has seeped through something.