Intergalactic travel is space travel between galaxies. Due to the enormous distances between our own galaxy and even its closest neighbours, any such venture would be far more technologically demanding than even interstellar travel. While luxons (massless particles such as photons) would take approximately 2.54 million years to traverse the 2.54 million light-year wide gulf of space between Earth and Andromeda Galaxy, it would take an arbitrarily short amount of time for a traveler at relativistic speed (due to the effects of time dilation; the time experienced by the traveler depends both on velocity, being anything less than the speed of light, and distance traveled (length contraction).
Intergalactic travel, as it pertains to humans, is impractical by modern engineering ability and is considered highly speculative. It would require the available means of propulsion to become advanced far beyond what is currently thought possible to engineer in order to bring a large craft close to the speed of light. Unless the craft were capable of reaching extreme relativistic speeds, another obstacle would be to navigate the spacecraft between galaxies and succeed in reaching any chosen galaxy, star, planet or other body, as this would need an understanding of galactic movements and their coordination that is as of yet not understood. The craft would have to be of considerable size, without reaching speeds with noteworthy relativistic effect as mentioned above it would also need a life support system and structural design able to support human life through thousands of generations and last the millions of years required, including the propulsion system—which would have to work perfectly the millions of years after it was built to slow down the machine for its final approach. Even for unmanned probes which would be much lighter in mass, the problem exists that the information they send can only travel at light speed, which would mean millions of years just to receive the data they send.
Current physics states that an object within space-time cannot exceed the speed of light, which seemingly limits any object to the millions of years it would at best take for a craft traveling near the speed of light to reach any remote galaxy. Science fiction frequently employs speculative concepts such as wormholes and hyperspace as more practical means of intergalactic travel to work around this issue.