Jesus defined his ministry in Luke 4:16-18:
The Spirit of the Lord is upon me, for he has anointed me to bring Good News to the poor. He has sent me to proclaim that captives will be released, that the blind will see, that the oppressed will be set free, and that the time of the Lord's favor has come.
Jesus came to help those who were poor and oppressed. Everywhere he went he healed people (Matthew 8). He didn't just heal people physically, but spiritually too. Matthew 8:16-17 describes how Jesus healed those who were demon possessed and healed the sick to fulfill the saying of the prophet Isaiah, "He took our sicknesses and removed our diseases." However, if you look at Isaiah 53:4, the passage that Matthew translates as sicknesses and diseases, it says, Yet is was our weaknesses he carried; it was our sorrows that weighed him down.
Many people's problems are not physical but emotional, spiritual or psychological. Can Jesus heal these problems too? Of course. "Inner healing" is the name usually given to this. (Over the years, some have called it healing of the memories.)
Part of my study into this area looked at how we view man. Usually the terms, spirit, soul and body are used. People often quote Scriptures such as 1 Thessalonians 5:23 (may your whole spirit and soul and body be kept blameless…) to verify this, and indeed this concept is a very helpful tool. But most commonly, the Bible just refers to the inner man and outer man. Other words are usually used for the inner man, such as heart or spirit (eg Daniel 7:15, 1 Corinthians 6:20).
The outer man is obvious. The inner man consists of the soul (mind, emotions, will etc) and spirit. The Bible itself says that it is difficult to distinguish between the soul and spirit–in fact it takes the word of God to do so (Hebrews 4:12).
Jesus heals the inner man–hence, for want of better terminology I will use the term "inner healing" to describe the process that happens when Jesus heals the inner person.