One longstanding Christian interpretation is that death entered human experience immediately, even though physical death did not occur at once. Adam and Eve became subject to mortality, and their eventual physical deaths were the consequence of their disobedience.
Other Christian commentators emphasize spiritual death. When Adam and Eve sinned, their relationship with God was profoundly damaged. They experienced shame, fear, and separation from the unhindered fellowship they had enjoyed in Eden. Their expulsion from the garden dramatically expressed this broken relationship.
These explanations are not mutually exclusive. Scripture frequently speaks of death in both physical and spiritual terms. Paul later taught that sin entered the world through one man and death through sin. The New Testament also describes those separated from God by sin as spiritually dead, even while physically alive.