It looks like your plant has a fungus. There are a few actions you can take to possibly save your plants. First, remove all infected leaves. Then make sure your pots have drainage holes. Too much water is a breeding ground for fungi. Keep the plants in sunlight, make sure there is good air circulation, and always be careful water does not splash on the leaves when you water the plant. If you wish, you may also spray a fungicide weekly. Read the labels carefully to be sure the one you get is appropriate for basil. For more information, please read: Basil | Home & Garden Information Center (clemson.edu) and/or Basil | Diseases and Pests, Description, Uses, Propagation (psu.edu)