"Spiritual" is often used in a non-religious sense to describe something that feels meaningful. People might describe hearing a piece of music or seeing a magnificent view as a spiritual experience. See, for example, the definitions in this page.
Or, it can be used very broadly of any experience of the supernatural. It is sometimes described as belief in something beyond yourself. The Hindu or Wiccan can be described as spiritual. In one sense that is true; they engage with spirits.
However, biblically "spiritual" is far more specific. In some places it is contrasted with "carnal" and even Christians can be carnal. The spiritual person has come into a relationship with God through faith and repentance and is living in relationship with God. The carnal person satisfies the desires of the flesh. The spiritual Christian has died to him/herself and lives to please God.
What is Spiritual Life And Why is It Important? - Kristi Walker (Christianity.com)
Includes the following definition: "Spiritual life quite simply is the life lived in and with God. Just as physical life starts when our physical heart starts beating, our spiritual life begins when our spiritual heart starts beating. More specifically, spiritual life begins when we are "born again".
Before anything else, spiritual renewal is about knowing God - experiencing the presence and power of God.
I keep asking that the God of our Lord Jesus Christ, the glorious Father, may give you the Spirit of wisdom and revelation, so that you may know him better.
Ephesians 1:17
Christ-likeness
Some aspects of obedience are expected of all who follow Jesus. They are non-negotiable and are summed up in the two Great Commandments:
Love God with all your heart, soul and mind
Love your neighbour as you love yourself
Discipleship is defined by Jesus as learning to obey all he commanded (Matthew 28:20). All Christian disciples are to increasingly obey all of Jesus' commandments.
Some aspects of obedience depend on a person's own calling and gifting. Christians serve in different areas. Their love for God and others will be seen in their evangelism, church leadership, care of creation, social justice, intercession, healing etcetera, etcetera, etcetera.
But no Christian can obey Jesus without the power of the Holy Spirit. Jesus said that without Him we could do nothing (John 15:5). The Holy Spirit is given to empower us for mission (Acts 1:8) and without Him mission is impossible. Jesus told the disciples to not even try until they had received the Holy Spirit (Luke 24:49; Acts 1:4). Just as character transformation is a work of the Holy Spirit (as seen in the Fruit of the Spirit), effective service requires the power of the Holy Spirit (as seen in the Gifts of the Spirit).
"Renew" means that something is being made new again. It is a returning to the original after a time of decay or distraction. It implies something has been lost.
Spiritual renewal might be an individual experience, corporate as a church is renewed or even societal (periods of revival or awakening).
Arguably, an individual could experience renewal and return to something that he/she never knew but is true of people in general. A conversion is a renewal of the relationship with God that was evident in the Garden of Eden. A church experiencing renewal might discover things that have never been part of the life of that church but are a return to the biblical understanding of the church.
Several terms are somewhat synonymous. "Spiritual renewal", "revival", and "awakening" all overlap. Revival tends to describe a spiritual renewal that is wide-spread enough to impact society as well as individuals and the church. Obviously, renewal speaks of being made new again, revival speaks of receiving life again and awakening speaks of waking up (becoming conscious of God again).
Spiritual Renewal Lessons from Eugene Peterson - (Center For Church Renewal)
What Does The Bible Say About Renewal? - (Got Questions)
Spiritual Renewal - (Bible.org)
focuses on salvation as the most fundamental form of spiritual renewal (new creations transformed from death to life)
Spiritual Renewal - (Orthodox Christian Laity)
defines spiritual renewal as "the process of growth and transformation into the image of God"
Spiritual Renewal As Expressed in the Christian's Life - Forrest Bivens
seeks to describe what a spiritually renewed person looks like