It means the state or property of being porous, or refers to the ratio of pores or voids to the total volume of something. For example, clay pots are better than plastic for growing many plants because of their porosity.
Porous means letting through water, air etc. It can also refer to breaches of security or leaking of information.
Pour us a drink and poring over manuscripts are entirely different, even if the latter does reveal plot holes.