If you do not appoint a guardian, then the other parent who has legal guardianship would look after the children. If not, then someone will need to apply to the court to become the guardian. The person may not be the best choice or may not have the means to bring them up.
The court process may also take some time and your children may end up staying with social services before the court confirms the legal guardian. So appointing a guardian is very important, and our online Will service can assist you with this.