Praying for others expresses our concern for them. It is our request to God to grant our wish in favour of someone. Obviously, the wish may or may not be granted depending upon God's grand scheme and divine plan about human beings. But what counts before God is our sincerity for a fellow human being.
So, just as we pray for our own selves for our needs and wishes, it is very desirable to draw a list in our mind of all those who we know are in some need or affliction. Thus for example, we can pray for the forgiveness of all the dear departed of our family and it would be better if we pray by naming each of them.
Similarly, we can pray for the health of the sick and ailing that we know around us keeping their names in our mind when we pray. We can also pray for those who are jobless and are hunting for jobs. We can pray for the boys and girls of our family who need good matches for marriage. The list is unending.
So before God let us cry
With that wailing teary eye
Prayers are gushing fountains
They can move mountains:
Lord! Take good care of the bitten
Shower thy mercy on the stricken