The phrase refers to a high socioeconomic status from birth, not just wealth. Despite his modest job, Adam's refined manners hinted he was born with a silver spoon in his mouth.
Pro Tip 2/3
Idiomatic Nuance
This idiom often implies a lack of understanding of everyday struggles by the person it's used for. He had no idea how to do laundry; he was born with a silver spoon in his mouth.
Pro Tip 3/3
Cultural Perception
Culturally, the phrase might be used with a tone of envy or disapproval. Jenny was born with a silver spoon in her mouth, unlike us who worked for everything.