Christian heterosexual human males that were born male, and believes himself to be male, (so no puppets or androids) show affection towards another male who lived 2000 years ago named Jesus, who is also the one and only Son of the God of the Christian tradition. This love is one of admiration and worship, not necessarily sexual in nature.
Real men love Jesus, so I don't think that Pinocchio counts.
Same concept used with Secret Santa during Christmas where everyone draws a name out of a hat and gifts the other person. Secret Jesus is used when participating with a Christian family primarily because Santa is believed to be of the devil and the gift exchange happens on New Year because Christmas Day is reserved for Jesus.
Person 1: "Hey, are you doing Secret Santa with your family this year?"
Person 2: "Nah, my family are fanatical Christians. It's more like a Secret Jesus gift exchange.