The mission of the U.S.S. Enterprise-D is to seek out new lifeforms, and one of the strangest ever encountered is the mysterious humanoid known as the Traveler.  Tall, with pale skin, three fingers on each hand, silver hair and a heavy eyebrow ridge, the Traveler first boards the Enterprise posing as the assistant to a Starfleet propulsion specialist who is adjusting the Enterprise's warp engines.  A miscalculation by the Traveler catapults the starship first to a galazy more than 2 million light-years away, and then to a region of space where thought and reality are interlinked.  The Traveler's ability to sense and manipulate the connection between time, space and thought go far beyond 24th-century science, and the alien's destiny becomes strongly linked to that of another Enterprise crew member.

The Traveler has an intense curiosity about other beings, as well as a special knowledge of propulsion that he trades for passage on Starfleet vessels so that he might experience their reality.  The alien says that thought is the basis of all reality, and that he is able to act as a lens that can focus the energies of other people's thoughts into himself.  He tells Captain Picard that young Wesley Crusher and a few like him are why he travels: Wes is apparently a prodigy with immense potential to understand the interconnection of time, space, and thought as few humans can.  Bolstered by the positive thoughts of the Enterpirse crew, the Traveler is able to return the ship home before fading away.

The Traveler returns three years later to help Wesley rescue his mother, Dr. Beverly Crusher, from a static warp bubble that trapped her in another reality.  With the Traveler's assistance, Wes is able to focus his mental energies and create a stable gateway to allow Crusher to escape.  The Traveler tells Wes that he has a power to open himself to time and space in a way few of his species can.

The Traveler next appears to Wesley as the young man is about to graduate from Starfleet Academy.  Wes is uncertain about pursuing a Starfleet career, and the Traveler offers to guide him in undertaking a journey where, truly, no one has gone before: exploring planes of existence where thought and energy combine, where laws of time and space are completely different.  Wes departs with the Traveler to pursue their mutual destiny.