1 Corinthians 15:45
And so it is written, The first man Adam was made a living soul; the last Adam [was made] a quickening spirit.
Note 14 at 1Co 15:45: Paul quoted from Ge 2:7 where God "breathed into his [Adam's] nostrils the breath of life; and man became a living soul" (brackets mine). This refers to how God originally created mankind. Man's body was created, and then God breathed His Spirit into man and gave life to man's soul. The term "living soul" refers to the unique spirit-and-soul combination, or what the Scripture often calls the "heart" (see note 3 at Mt 12:34 and note 6 at Mr 11:23). Man was a soul, which derived its power, or life, from the spirit God had given him (Jas 2:26).
The second part of this verse states, "The last Adam was made a quickening spirit." This is speaking of Jesus after His resurrection and is in contrast with how Adam was created. Jesus became a living soul like Adam when He was incarnated in human flesh, but upon His resurrection, He returned to being a Spirit, as He had always existed (Joh 4:24).
This is not a spiritual existence the way some people think. Jesus does have a tangible body (see note 13 at 1Co 15:44), but it's spiritual, not natural (1Co 15:44). His present existence, and our future state in our glorified bodies, differs from Adam's existence in the sense that the spirit dominates instead of the soul. We will no longer be living souls but quickening spirits like Jesus (1Jo 3:2).
Note 15 at 1Co 15:45: This is the only time in Scripture where Jesus is referred to as the last Adam. However, it is very appropriate. Adam was the first man to experience death. Jesus was the first man to experience everlasting life. Through Adam's actions, all his children died. Through Jesus' actions, all His children live (Ro 5:18). Adam and Jesus are the only two men who never had earthly fathers and the only two men who knew what it was like to be sinless. Therefore, there is a very close comparison between the two.