The more root-bound these plants are, the more babies they produce. The more babies on the plant, the more water the plant uses. Remove the offshoots and put in water or soil; it will mature into a new plant soon.
Spider plants are commonly variegated with a white stripe in the middle, but can come with a reverse stripe, or solid green leaf. This is one hardy plant. Most problems arise from over watering. You will start getting black tips with a yellow halo, then whole black lower leaves. So, they need to be dry between watering. Keep an eye on the foliage it becomes pale and droopy when it's ready for water. The root system is large and tuberous, and can store water longer than most hanging plants.
As the offshoots mature, they should be removed from the main plant. The bigger the babies get, the more strain they put on the mother plant. They can be cut off and put directly in moist soil or just put in water. Their roots are already formed, so starting another plant is extremely easy. To remove babies trim the stem off both the mother and the baby. It looks better if there are no stubs showing.