Explain regeneration?

Nobody doubts that they have a phsyche or soul or inner person, but many people doubt that they have a spirit distinct from the soul. The bible in 2nd ephesians explains that this is because the spirit is dead, slain in trespes and sins. When a person comes to God through the cross, turning away from sin God brings this spirit which was dead back to life when He imparts to them the Holy Spirit. Is this what christians mean by being born again?