To say that God is personal means that God can be 'related to' as a person e.g. a God who answers prayers or gives people religious experiences can be experienced in a personal sense
Some people say they have a relationship with God. A personal God would be immanent within the world. God as Father, Son and Holy Spirit are thought of as immanent and personal
Moltmann's 'social' account of the Trinity emphasises the three persons of the Trinity existing in a community of mutual self-giving and receivinglove. This offers a model for human personal relationship.
Christians who follow Catholic NaturalMoralLaw believe that moral standards are not just a matter of opinion, they are objective and given by a personal God