The person you are greeting will be safe from you
The greeting of peace (as-salamu ‘alaykum) has many meanings.
One of these meanings is that the person you are greeting will be safe from you (from your tongue, your heart, and your hand) and that you will not transgress against that person with your words or your deeds.
This greeting is also a prayer for peace, safety, mercy, and blessings.
We should take these noble meanings, which we so often say with our tongues, and make them our way of life in our dealings with other people.