O'Neill's play takes place during a twenty-four-hour period (or less) in which the problems of the Tyrone family are laid bare in stark detail. It is thus a "journey," as the title indicates, beginning in seeming placidity as the family start their day, and ending in virtual catastrophe the night of that same day .
Each of the characters is living in a self-created world of delusion. As the long day progresses, the family members are slowly forced to confront the reality of their failures. Mary is a drug addict; she has thought to hide this from her husband and sons but is ultimately unable to. Edmund has consumption (tuberculosis); he and the others have suspected this, but Mary, especially, has been in denial about it until the end of the play when Edmund announces it to her. Jamie, Edmund's elder brother, is an alcoholic and a failure in life. Tyrone is an alcoholic as well, reliving his past glory as an actor and refusing to accept the negative things about his wife, his sons, and himself. The entire family are in denial about all these facts; the title of the play refers to the journey, taking place from morning through to night, of their being forced out of the cocoon of denial to recognize the harsh reality of their suffering.
The title also symbolises the "journey" through which addicts go through on a daily basis. All of the Tyrones are using drugs or alcohol. For people with addiction problems, every day is a repetitive process in which they drink or use over and over, until night finally brings sleep. It's thus possible O'Neill intended the title as a metaphor for the disease of addiction.