If your audio signal is suffering from hum noise, it is likely due to a 'ground loop'. This is happens when a multiple electronic devices are connected and one device has a 'lower resistance to ground'. When this happens, the ground signal for the entire network of connected devices are combined and the electrons are all expelled through the ground pin on the power plug from the device with the lowest resistance. This massive flow of electrons causes an affect on the Hot/Cold signals, heard as what we call 60Hz hum. Most modern devices have a similar 'resistance to ground', so ground loops are not as common as they once where are more common when using old equipment with newer equipment.
To solve the issues or mains hum / 60Hz hum, you need to isolate the offending electronic device that has the "lowest resistance to ground" (i.e. the one causing the problem). Isolating is often done by using a device with a transformer. A transformer allows Hot/Cold signals to pass, but does not allow the electrons from the ground signal to pass through thus removing the hum. There are dedicated hum eliminators that really just have inputs and outputs, and a isolating transformer in between. Such devices include the ART DTI. Also passive DI boxes also include "transformers", and thus can also isolate ground hums. Note, that most active DI boxes have no transformer, and won't stop ground hum.
Another option for removing electric hum, is to simply "lift" the ground signal. Some devices have "ground lift" switches to enable this to be activated easily on the device. Or a simple ground lift adapter can be used, which basically just disconnects the ground signal so it does not terminate anywhere. Be careful with ground lifts, as some devices require the ground signal to be connected. Condenser microphones are such a device, as phantom power is required to operate condenser mics and the ground must be connected for phantom power to pass.