Travel Gates are a warp points that appear in The Legend of Zelda: Breath of the Wild. They are warp gates created via ancient Sheikah technology that at designed to be used in conjunction with the Sheikah Slate which allows one to teleport to any activate Travel Gate.
Travel Gates commonly appear on Shrines and Sheikah Towers which become active once Link has activated the corresponding Shrine or Sheikah Tower with the Sheikah Slate. Shrines only have to be opened using the Sheikah Slate in order to activate their travel gates, thus Link does not have to complete a Shrine's trial in order to use its Travel Gate (thus Link can simply use the Sheikah Slate to open the Shrine to activate its gate which allows him to return to the Shrine at any time once he is prepared to take on its trial). However Sheikah Towers must be climbed and their map data obtained in order to use that Tower's travel gate, though Link can activate and use other Travel Gates even in areas he does not have Sheikah Tower Map data for. Once activated Link can fast travel to these places by selecting its gate on the Sheikah Slate's map. Additionally Travel Gates can also be found at the Hateno Ancient Tech Lab and Akkala Ancient Tech Lab which can be activated once Link restores power to each labs with the Blue Flame from the Ancient Furnaces located in Hateno Village and Deep Akkala. Once gate is selected Link's body is converted into pure energy which rematerializes at the selected travel gate.
The first Travel Gate Link activates is the Travel Gate inside the Shrine of Resurrection which automatically activates after Link opens the door in order to leave the shrine after waking up from the Slumber of Restoration.
The icon of active Travel Gates are blue while inactive Travel Gates Link has discovered will be orange on the Sheikah Slate map. If a Shrine, Tower, or Tech Lab is found its Travel Gate will appear on the Sheikah Slate's map even if the map for the area the Travel Gate is found has not been obtained, thus allowing Link to use the orange and blue gates as landmarks when he lacks that map data for those areas. Link is unable to warp to inactive gates and some gates may require him to take part in or complete certain quests such as "Locked Mementos" & "Robbie's Research" or Shrine Quests such as "The Perfect Drink" (which Link must complete in order to activate the travel gate of the Misae Suma Shrine). Activating all travel gates gives Link multiple warp points to choose from which make traveling around Hyrule faster or makes returning difficult or hard to reach locations easier such as the Great Plateau, Korok Forest, or Hyrule Castle. Most villages and Stables are located near Shrines which means activating these Shrines grants Link the ability to warp to there travel gates which allows him easy access Stables, Inns, or shops allowing him to use their services to restock and rest.