Something absorptive has the quality of soaking up liquids. Paper towels are advertised as being extremely absorptive, but often a washcloth or sponge works even better to soak up spills.
You can buy special towels that are more absorptive than usual for drying your hair — they're made to absorb water. or soak it up quickly. You can also use this adjective in a figurative way, especially when you talk about one thing taking in something else (like an absorptive mind that takes in information) or accepting something (like an absorptive country that allows many immigrants to enter). The Latin root is absorbere, "swallow up."