The swab is designed to collect residue from your bag/hands, etc. which the machine analyzes, looking for certain chemicals that are common in items that could be a threat to aviation. What exactly they are looking for is SSI (Sensative Security Information).

When a TSA officer wipes your bag with a small white cloth, they are performing an Explosives Trace Detection (ETD) test. The cloth is a specialized swab that picks up microscopic particles of chemical residues. The officer then places this swab into an Ion-Mobility Spectrometer (IMS) machine, which analyzes the particles for nitroglycerin, nitrates, glycerin, and other chemicals found in explosives or improvised devices. This is often a random check, but it can be triggered if your bag's contents appear "dense" on the X-ray. You should not panic if you are selected; common items like certain hand lotions, heart medications, or even garden fertilizers can cause a "false positive." If the machine alarms, you will simply be subject to a more thorough manual search of your bag and a pat-down to ensure the residues are non-threatening.