Babysitting is an activity which crosses the divide between the spiritual and the physical. Spiritually it suggests the nurturing, caring side of the personality or that part which is ready to take responsibility for others.
Psychological / emotional perspective: Viewed from a psychological perspective, babysitting in dreams suggests that there may be a part of our personality which has not yet matured fully and needs looking after.
Material aspects: For many teenagers, babysitting is an ordinary, mundane activity and thus provides a dream scenario in which they can work out their attitude to other responsibilities in their lives.
For others it may highlight their attitude to family responsibilities or to parenthood.