As Calvinism became mature, the meaning of regeneration became more specific: what God does to produce spiritual life in a spiritually dead person. This is to be distinguished from the person's contribution to the whole process of conversion. Calvinism teaches Total Depravity, meaning that a person is spiritually dead at birth (because of original sin) and consequently do not have the ability to make a decision for faith in Jesus before God performs this regeneration act. The act is usually preceded by Calling (see Calvinist ordo salutis), which is best likened to Jesus calling Lazarus from the dead. In this restricted sense, we may wonder why the term is not simply "generation".
But when we survey the theological history of regeneration prior to Calvinism, regeneration was usually linked to baptism, and that is why the term baptismal regeneration is common in other denominations (see wikipedia). Baptism clearly implies being reborn: we die to our old self and God resurrects us to the new life. As we participated in Adam to die spiritually, we participated in Jesus to be resurrected. With this linkage, the term "regeneration" makes sense.
For scriptural support, theologians cite what Jesus taught Nicodemus of needing to be "born again" in John 3:3-8, as well as what Paul taught in Titus 3:5 which links being born again with baptism. In Titus 3:5 the word used is palingenesia which originally means re-creation (see wikipedia), which is then translated in theological literature to the Latin word regenerationem from which came the English word "regeneration".