When Christians say that Jesus died for our sins, what do they mean? Give the three elements of the Holy Trinity, according to Christians and provide a common analogy that explains the concept of the trinity as being three elements but one overarching understanding

 

Answer:

When Christians say that Jesus died for our sins, they simply mean that Jesus paid the penalty for each individual's sin in order to right the relationship between God and humanity, a relationship damaged by sin. 
Elements of the holy trinity
The doctrine of the Trinity means that there is one God who eternally exists as three distinct Persons — the Father, Son, and Holy Spirit. Simply stated, God is one in essence and three in person. In the Christian faith, the three points of the Trinity knot represent the Holy Trinity of Father, Son and Holy Spirit (Lourié, 2016). Occasionally, you may see the Trinity knot enclosed within a circle as a means of emphasizing unity or eternity. When we discuss of the Holy trinity, we are aware that trinity means three, and thus, Holy trinity comprises of the Father, who represents God, son who represents Jesus and the holy spirit. Throughout the holy book, the Bible, we are told and convinced that God is still one. 
References  
Lourié, B. (2016). Nicephorus Blemmydes on the Holy trinity and the Paraconsistent Notion of 
Numbers: A logical Analysis of a Byzantine Approach to the Filioque. Studia 
humana, 5(1), 40-54.