Your child is now able to understand things around him or her and so is also able to feel emotions like fear, anxiety. It is common for them to feel afraid of animals like dogs, cats though some of them get attached to them if they have pets. At this age they might also have fear of darkness, particularly when they are left alone in the dark. Other children might fear fires, thunder storms or heights.
What you need to know
These fears are mild and even if they intensify they will gradually go away on their own. If the fears become extreme they might develop into phobia at which stage it will hinder the child’s daily chores and activities. Like a dog phobia might make the child not go out to play, a thunderstorm phobia might make them stick to the house during rains and not enjoy playing, etc.
Some children at this age might fear about meeting new people due to their shyness which if not eased out, may hamper their socializing with other kids at parties or schools. Separation anxiety is also one of the fears a child of 7-8 years goes through. The parents have to recognize this since changing neighbourhoods or leaving the child in day care might intensify this anxiety in children. The children might show their unwillingness to do their activities by complaining of headache, stomach ache etc when they are having fear of any kind. Your 7-8 year old can understand the concept of death also and while some take it lightly others might retain the fear and become depressed.