No, activated carbon isn't necessary for aquarium filtration. What activated carbon can do is remove organic molecules that causes odor and water discoloration, medication, chlorine and certain heavy metals such as copper. In a normal situation, activated carbon is unneeded as it isn't doing anything your water conditioner and regular water changes aren't already doing. However, there are certain situations that can warrant the usage activated carbon in your filter. It is useful for removing medication after your fish has been treated, as well as removing unwanted water coloration that can be caused by the addition of driftwood to your aquarium.
So why is activated carbon often included with aquarium filters, and recommended by manufacturers to replace monthly? Because it's just a simple money grab, and an easy way to sell you something that you don't need.