In the larger passage in which this injunction is contained, Matthew 5:43-48, Jesus taught his disciples that they must pray for their enemies in order to gain the reward of becoming something like God. He did not explain exactly what that means, which leaves us with some "running room" in our understanding and application of the command itself.
So, why love and pray for our enemies? Basically, as long as our enemies remain our enemies they own us. They have our attention and dominate our emotional state. They infect us with feelings of disgust, anger, hatred, and fear. They have an internal power over us that can easily turn us into what we think they are. To allow someone to be our enemy is to give them great power over us. The same is true even for those that we merely don't like or irritate us—to the extent that we let them get to us, to that extent they own us.
Praying for our enemies, if done with integrity, takes the poison out of us and allows us to be at peace with ourselves. It also opens the door to the possibility of being at peace with them as well—depending on factors that we don't have control over. The scales fall from our eyes. Our hearts are less encased in ugly feelings. As God is love, so we drift in the direction of love. As God lies at the heart of peace, so we sink slowly into the realm of peace. We enable the prayer, "Thy kingdom come, thy will be done." Yes, this is easier said than done, but it remains doable, and our own peace of mind depends on our being able to love and pray for our enemies. And, no, we don't have to become naive or overlook seriously bad behaviors, it is just that we no longer let all of that own us and destroy our own sense of inner peace.
And "enemies" here need not mean individuals. It can also mean an addiction, for example, which for millions and millions of people is their greatest enemy. It can mean the poisons implanted in us by an abusive relationship, which itself is over. It can mean our prejudices against another race or class of people.
