What is the First Death?

Hebrews 9:27 states:

It is appointed for man to die once, and after that comes judgment (ESV).

The judgement (if adverse) is easily equatable to the "second death," implying that the first death is thing to which all men are appointed once. Since Genesis 3 indicates that all men are under the curse of physical death, that seems the most likely candidate.

I'm sure that there are people who think otherwise, but you didn't specify a perspective,so I'm going to go by answering it from what is the most common understanding in my personal experience. By that I mean not my own personal opinion, but rather the understanding that every sermon I've heard, or every exposition I've read seems to think.

With that qualifier out of the way, I believe that the most common understanding is that it refers to the physical death of the body.

In context it makes sense, since we're looking at a passage talking about the judgment of the resurrected, which implies that they suffered physical death already.

For an external source, I'll use this post form Moments With The Book

The First Death

Let's notice a few facts about the first death. Every person has a body, a soul, and a spirit. "And the very God of peace sanctify you wholly; and I pray God your whole spirit and soul and body be preserved blameless unto the coming of our Lord Jesus Christ" (1 Thessalonians 5:23). The human spirit is that God-conscious part of a person that distinguishes him from the animals. It includes both knowledge and judgment (Mark 8:12; 1 Corinthians 2:11). The soul is that part of a person that is the home of the affections—right or wrong—of love, hate, lusts and even of the appetites of the body (Job 23:13; 1 Peter 2:11). The body is the earthly house in which the spirit and soul dwell. At death a person's immortal (never-dying) spirit and soul leave the mortal (subject to death) body. This is the first death, or physical death.

A believer's spirit and soul go immediately into a place of blessing at the time of death. This is evident in the well-known account of the thief on the cross. This repentant thief owned that he was getting what he deserved, and confessed Jesus as Lord, believing God would raise Him from the dead: "Lord, remember me when Thou comest into Thy kingdom." The wonderful answer from the Lord Jesus was, "Verily I say unto thee, today shalt thou be with Me in paradise" (Luke 23:39-43). This blessed truth of the believer being with the Lord Jesus immediately after death is also repeated in 2 Corinthians 5:6-8 and Philippians 1:23.

It is especially comforting to the Christian to see that the Lord Jesus did not refer to the death of the believer as death. The Bible speaks of it as the body falling asleep (see John 11:11-14 and 1 Thessalonians 4:13-18). Death is the penalty of sin. The believer in the Lord Jesus does not come under the penalty of sin because the Lord Jesus took that penalty when He died on Calvary's cross.

An unbeliever's spirit and soul go immediately into a place of torment at the time of death. The Lord Jesus tells us of this awful torment in His account of the rich man and Lazarus (read Luke 16:19-31). "And in hell he lift up his eyes, being in torments, and seeth Abraham afar off, and Lazarus in his bosom. And he cried and said, Father Abraham, have mercy on me, and send Lazarus, that he may dip the tip of his finger in water, and cool my tongue; for I am tormented in this flame" (verses 23,24). The rich man was in torments, not because he was rich, but because he had not believed God's Word. People may disregard this account, but it came from the lips of the One who suffered sin's agony and torment on Calvary's cross so that no one ever would need to experience this awful judgment.

Also, this article from the Forerunner Commentary goes into great detail about the various meanings of death,and agrees with the above.

We must always remember that our Creator, the Master Craftsman who made everything of the highest quality (Genesis 1:4-31), built death into man's design. He did this for good reasons. Surprisingly, there really are good and positive purposes behind both the "first death" and the "second death" (Revelation 2:11; 20:6, 14; 21:8). The first death is the one with which every person is familiar—the one everyone must face. This death terminates the physical life of every human being who lives during the 6,000 years allotted to man.

I could find immeasurable other supporting references, but I'll stop there.

I'm not saying it couldn't be any of those other things, but I've yet to run across another interpretation so my final answer is that the most common understanding seems to believe it means physical death.