There are several emotions portrayed, but the main two focused on are Joy and Sadness. Joy wants everything to be fun and happy. Sadness focuses more on the gloomy side of life.
What we come to see is that we need both to fully understand life.
I have both joy and sadness in my life. I cannot experience the full wonder and awesomeness of the good times unless I have understood the crushing weight of losing something.
Without experiencing the wonder of a sunrise, I do not understand the fear of being in the dark.
Without having been loved and loving someone, I can not understand the depth of despair that comes from losing that loved one.
What Inside Out teaches us and shows kids is that it's ok to have feelings. And it's ok to let those feelings out.
We may all have different ways of expressing those feelings. And that's ok too. But we all need to let the feelings out. To let ourselves be happy but also gives ourselves time to mourn.
It is both that help shape us and determine who we are.