Separation anxiety is when young children get upset when their parents leave them with someone else. It typically develops after 8 months of age when children develop object permanence and realize when their parents are not with them. Many children first experience separation anxiety when they are left with a babysitter or brought to preschool. While a child’s attachment to a mother and father is important, it is also important that children become independent of their parents.
To answer the second part of your question, how children with separation anxiety behave as adults, the article posted says “it’s only temporary.” Most kids outgrow separation anxiety. If they do not outgrow it by later into preschool or elementary school, they may have separation anxiety disorder; then a doctor should be consulted.