Jesus interprets what he means by loving your enemies and turning the other cheek:
32 “If you love those who love you, what credit is that to you? Even sinners love those who love them. 33 And if you do good to those who are good to you, what credit is that to you? Even sinners do that. 34 And if you lend to those from whom you expect repayment, what credit is that to you? Even sinners lend to sinners, expecting to be repaid in full. 35 But love your enemies, do good to them, and lend to them without expecting to get anything back. Then your reward will be great, and you will be children of the Most High, because he is kind to the ungrateful and wicked. 36 Be merciful, just as your Father is merciful. Luke 6
It’s about Mercy. So if you want to be a representative of the Father here on earth, you can show how the Father is merciful by being merciful yourself. That means you do not seek escalation and revenge. Loving your enemies was the turning point in moving the entire world away from being a society based on retribution (an eye for an eye) to a new society based on mimicking the mercy of the Father here on earth.
One example could be the forgiveness of debts to third-world countries.
Another could be the muted response that Israel usually has after being attacked.
On a personal level, if one visits the jail cell of a criminal who wronged you to tell that criminal you forgive him, that would be an example.
And BTW, you can only be merciful when you are in a position of power and choose not to use it. You can’t count it as being merciful if you simply submit to an enemy whom you cannot defend yourself from.