"Alav HaShalom" means "The Peace is upon him", "Shalom" referring to HaShem. This phrase is used in reference to someone who is no longer alive.
 The entire pasuk states, “Trust in HaShem and do [that which is] good, dwell in the land and shepherd belief [in HaShem].” (Tehillim: 37; 3) RaSh”I explains “shepherd belief” to be “sustained by belief”.
RaSh”I explains the pasuk as follows:
Trust in HaShem: “And do not say, ‘If I will not rob and steal, or if I will give charity to a poor person, with what shall I sustain myself?’”
And perform good: Then you shall dwell on the land with longevity.
And shepherd belief [in HaShem]: “You shall eat and earn your livelihood from the reward of the belief, for you have believed in The Holy One, Blessed is He, to rely upon Him and to perform good.”
From the above pasuk, we learn that the individual benefits from having belief in HaShem that by following the Torah, the person will benefit. The person should not think that avoiding charity and stealing will be what benefits him. The world is run by HaShem, and the person who follows The Torah is the one who truly benefits.
 This teaching is found in maseches Sotah, Chapter 8, in the end of Halacha 13.