James 5:14 Is anyone among you sick? Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord.
While we can pray for the sick without being present, nevertheless, when we go and pray in the presence of the sufferer, the prayer is heartfelt and fervid, and the love of one another is so strongly felt as well. It is important to note that we should not assume the elders have a special anointing or gift of healing but rather the elders are representing the whole church in being present with the sufferer.
As we are flesh and blood as well as spirit, the sacrament of oil anointing gives the sufferer a heartfelt presence of the Spirit of our Lord, though we have to be reminded again that there is no magical power in it. Psalms 23: 5.
The sheep in the Middle East are often annoyed by the numerous flies flying around them. And when the shepherd anoints their head with oil, it soothes them so much that they do not bash their heads in frustration against the bushes. When a baby is feeling discomfort and cries, the physical touch of the mother is so soothing and comforting. So likewise, when we feel the presence of the Spirit of our Lord amidst intense suffering, the close communion with our Lord in His soothing touch comforts and uplifts our spirit man.