Space travel was travel from one celestial body to another.
Development of the ability to travel through space was regarded as one of the first real steps species took in their development. The Time Lords developed space travel when "the universe was half its present size." (TV: Genesis of the Daleks)
Methods
For most species a vacuum was an extremely hostile environment. Therefore, to travel to other worlds they needed to find a way of avoiding exposure to it. The most common way was building spacecraft. Mankind learned space travel by the mid-20th century; (TV: Day of the Moon) other species did it billions of years before. (TV: City of Death)
Some planets, including the Earth in the late 21st century, had space elevators. (TV: The Waters of Mars)
A faster but more difficult method was teleportation — direct transmission from one place to another, whether by technological (TV: The End of the World, Boom Town, The Time Monster) or supernatural (TV: The Brain of Morbius) means. The Kitlings were able to teleport by willpower. (TV: Survival)
Biological abilities
Some species had a native ability to move through space without the use of technology. These species included star whales, (TV: The Beast Below) Wirrn, (TV: The Ark in Space) the Rutan Host (PROSE: Shakedown) and the Eight Legs. (TV: Planet of the Spiders)
Some species such as Time Lords could survive for a time in the vacuum of space, though they still needed to breathe oxygen. (TV: Four to Doomsday)
Humans and space travel
Humanity's first sojourn into exploring space began in the mid-20th century with the launch of several satellites. (PROSE: Alien Bodies) In 1969, humans first landed on the Earth's only natural satellite, the Moon. (PROSE: Blue Moon) A second party, who believed themselves the first, landed in 1970. (COMIC: Moon Landing)
By the 1970s or 1980s, England had its own space programme. The XK-5 space freighter was tested there and took off from Devesham. It went missing and was assumed to have hit an asteroid. (TV: The Android Invasion)