Perhaps the answer to the question: “What is spiritual death?” can best be addressed by asking what spiritual life is. We all know that prior to receiving Christ we were without the Holy Spirit. That is clear. I think we all understand in our “lost” condition the Holy Spirit was not dwelling in us. We were not “spiritual” but “natural” according to Scripture.
But the moment we believed and received the Lord Jesus Christ we were born again and we became spiritual because the Holy Spirit was now in us. In this sense we have been reborn…spiritually. I think this is where the phrases “spiritually alive/spiritually dead” come from.
It goes without saying we were certainly not born again physically (entering into our mother’s womb for the second time). I’ve always understood my rebirth is a "spiritual" rebirth. In this sense, prior to receiving Christ we were dead…spiritually, but after receiving Him we were alive…spiritually.
I see it this way:
No Holy Spirit = spiritually dead.
Indwelt with the Holy Spirit = spiritually alive.
1 Corinthians 2:9 But as it is written, Eye hath not seen, nor ear heard, neither have entered into the heart of man, the things which God hath prepared for them that love him.
2:10 But God hath revealed them unto us by his Spirit: for the Spirit searcheth all things, yea, the deep things of God.
2:11 For what man knoweth the things of a man, save the spirit of man which is in him? even so the things of God knoweth no man, but the Spirit of God.
2:12 Now we have received, not the spirit of the world, but the spirit which is of God; that we might know the things that are freely given to us of God.
2:13 Which things also we speak, not in the words which man's wisdom teacheth, but which the Holy Ghost teacheth; comparing spiritual things with spiritual.
2:14 But the natural man receiveth not the things of the Spirit of God: for they are foolishness unto him: neither can he know them, because they are spiritually discerned.
2:15 But he that is spiritual judgeth all things, yet he himself is judged of no man.
2:16 For who hath known the mind of the Lord, that he may instruct him? But we have the mind of Christ.
In my understanding, there is a clear distinction made between the “spiritual” man and the “natural” man in this passage. The natural man is not alive spiritually because the Holy Spirit is not in him. I have always believed that if a person is not alive spiritually by receiving the Lord Jesus Christ, he is dead spiritually…he must be born again.
By comparing Scripture with Scripture we see this thread of truth. I think some of us simply use the term “spiritually dead” to describe a person who has no life in Christ. Nothing more and nothing less. I’m in agreement with Brother George that the “spirit” of man is not dead; otherwise the body would be also. But I personally believe that man without Christ is “spiritually” dead because the Spirit of God is not living in him.