Teleportation is the hypothetical transfer of matter or energy from one point to another.
The user can teleport, or transfer matter (beings/objects, including themselves) or energy from one point to another without traversing the physical space between them. This can be achieved by various means, including causing the atoms/molecules to travel at light-speed, warping the space, or use quantum superposition, in which the user teleports by spatially rearranging the subatomic contents of a system. While teleportation may seem like it is simply for travel, it can be a valuable ability as it can be used offensively (and quite powerful, as a spatial attack) while offering superiority regarding movement speed and distance coverage. A skilled strategist/tactician can use it for many innovative manners.
Triggering The Power
Form the information gathered from the show, the user cannot be standing in order to teleport from one place to another. Number Five gathers up momentum and teleports while moving from one place to another. When he teleports to the chosen location his movement doesn't stop. The same goes for Lila Pitts, we do not know why she teleports the same way as Five, but it could be because she mimics the power as the user does.
Number Five has the ability to teleport both short and long distances, which he used frequently to evade Hazel, Cha-Cha and the Temps Commission. Despite being able to travel at will, multiple travels within a short time exhausted Five frequently, and the Handler noted that "even you Five have limits". In addition to teleporting himself, he is also able to take other people with him when he teleports, as shown when Diego teleported with him as they were running from Commission agents in The End of Something. He is also able to teleport objects without physical contact, which is shown in a flashback in We Only See Each Other at Weddings and Funerals, where he replaces a robber's gun with a stapler.
Lila is able to mimic the powers of the Umbrella Academy, at least while in close proximity to them and typically use these powers with great skill. During her battle against Number Five, Lila was shown to use his teleportation to fight against him and constantly used it to evade or sneak up at him with little effort.