It is our tradition to perform Aarati of those who are very dear to us because we wish the best for them. We are happy when they are, and want to take on their grief in their place so that they can remain happy.
Hence, by carrying out Aarati, we express our solidarity with them. This is why we encircle the Aarati lamp and then take our hands over our head, as if to signify that we are willing to take on their grief. After the Aarati, we chant the Mantra Pushpanjali in which we say a prayer for the happiness and prosperity of our loved ones.
We can perform Aarati of God as well as any of those who are very dear to us. Hence people perform Aarati of their Guru, husband, son, etc.