How does activated carbon trap impurities? I've tried and I've tried to find an answer to this all over the web, but I can't seem to find an in depth explanation.

To the best of my knowledge, activated carbon has a very microporous structure and uses a process called adsorbption to "trap" particles. This isn't very in depth though and I'd like to better understand the process of what's going from a scientific standpoint. How does the carbon/charcoal keep the adsorbed material attached or trapped within the carbon?
Never forget to interpret in terms of physical/chemical forces, by order of energy: van der Waals, hydrophobic (pseudo forces), hydrogen bonds, disulfide bridges, covalent, electrostatic (for the most frequent).

Indeed, in charcoal, there is a large number of $\pi$-electrons that can make bonds, in particular. And yes, the porosity is important. 

But perhaps could you have a look at Boehm H. P. Some aspects of the surface of carbon blacks and other carbons, Carbon, 1994, 32(5), 759-769. DOI 10.1016/0008-6223(94)90031-0.