Certified GKH Gardening Expert
This is, likely, a fungal infection. These are quite drought tolerant, and can develop an infection from remaining moist for too long without getting an adequate dry out.
You can treat this the next time that you have to water, which will be after it dries thoroughly. Just make a solution of 1/4 peroxide to 3/4 water. Water this in, and cut off any affected growth. This will only need to be done once, or any other time that this happens in the future.
This article will give you more information on the care of these: https://www.gardeningknowhow.com/houseplants/spider-plant/spider-plant-care-gardening-tips-for-spider-plants.htm