It indicates that your basement is humid and your ducts are likely uninsulated. Humidity is condensing on your ducts like it would on a cold glass of ice tea at a picnic. You should look at lowering the humidity in your basement. A dehumidifier would accomplish this. Adding duct insulation will keep the warm humid air away from your cool basement ducts. Conditioning the basement by adding HVAC to it would help as well. To be effective you'd need to have a air return pulling in basement air to run it over the AC coils. Your HVAC system may not be sized to handle your basement and just cutting in extra ducts and returns could unbalance your system and make the upstairs uncomfortable. I'm finishing my basement and added a separate unit for my basement rather than upsizing my first floor unit.
You might want to test to see where the humidity is coming into your basement, assuming you don't have visible wetness. Tape a piece of plastic or aluminum foil to the wall in several locations, you can also do it to the floor. Tape all four sides. If you get water trapped between the plastic/foil and the wall you have water vapor coming in through the foundation walls or floor. Making sure that your gutters direct the water away from the house will help. Exterior water proofing is the ideal, but as long as you don't have liquid water coming through the walls adding a coating like Dryloc or Thoro Seal can keep the water vapor at bay. If the water is condensing on the room side of the plastic the area you're testing is doing a good job of keeping the water vapor out and it is coming in elsewhere. I'm assuming here that your basement has a concrete floor. If the house is older there may not be plastic under the concrete. In newer homes (30 years or younger) it was common to have 6 mil plastic under the slab.