What is an explanation of Phoebe Palmer's belief in entire consecration, assurance, and service?

It sounds to me as though you need to discuss Palmer's famous "three step" approach to sanctification, a key aspect of Methodism. Palmer referred to these steps as entire consecration, faith (assurance), and testimony (service).
Phoebe Palmer was a Methodist evangelist who lived in the 1800s. She is well-known for participating in the "Holiness" movement and her doctrine of Christian perfection, achieved in three steps. She began to develop this theology after losing her children. When she cried out in prayer to God, she felt the harsh yet comforting reply that God called them home because she was focusing too much on her beloved children and not enough on service to God. Thus, when she learned to consecrate her entire self to God, her outlook improved. It was at this time she felt she achieved her sanctification, or "second blessing," and took to the pulpit to share this good news with others. To Palmer, the entire consecration she preached was a simplified version of Methodism founder John Wesley's doctrine of sanctification, or achievement of Christian holiness. Methodism espouses the idea that Christian holiness (also referred to as perfection or sanctification) is not the end goal of a Christian's life (other denominations posited that full sanctification was only achieved in heaven) but rather the start of one's faith journey. Initial sanctification was achieved at the moment of salvation, with a second sanctification (second blessing, Christian perfection, etc.) following. What Palmer did was bring a simplified version of this to the people.
This entire concept of a life free from sin was termed by Wesley as "entire sanctification." For Palmer, Christian perfection could be achieved through the baptism of the Holy Spirit. Additionally, one could find assurance of sanctification by reading the text of the Bible. For Palmer, that alone was sufficient for assurance, or what some might call faith. A life of entire service acted as one's testimony of sanctification. She believed that when God supposedly took her children, it was her initiation into entire service/testimony.
So, to sum it up, Palmer further developed Wesley's doctrine of Christian perfection, boiling it down to three steps: entire consecration, faith (or assurance), and service. Instant second sanctification could come when one was entirely devoted to God, assured of their salvation and sanctification through reading the Bible and entire service to God.
It is worth noting that many Christians, such as Lutherans, reject this second blessing concept, as they believe it goes against the concept of salvation or perfection by faith alone set out by Martin Luther. Wesley, Palmer, and other Methodists, assert these Christians, put too much emphasis on works as contributing to Christian perfection.
http://are.as.wvu.edu/phebe.htm

https://christianhistoryinstitute.org/magazine/article/holiness-fire-starter/