The context leading up to the parable is yet another argument with the Pharisees and teachers of the law. On this occasion their complaint is that Jesus has no sense of propriety about what kind of people a good prophet should associate with. In particular, he has an affinity for tax collectors and other such “sinners”.
In response to this accusation (that he welcomes sinners and eats with them) Jesus tells three parables:
1) The parable of the lost sheep
2) The parable of the lost coin
3) The parable of the lost son (aka the parable of the prodigal son)
All of these parables are stories about recovering something precious that is lost and then subsequently found. Jesus is thus implying that he associates with sinners because they are precious - but lost - and he wishes to recover and restore them.