The Phoenix Gate is a magical talisman that allows whoever uses it to travel through time and space. Its form is that of a small, flat, heater-shaped object with a phoenix design upon it.
It is one of the Three Keys to Power.
The origins of the Phoenix Gate are unknown, but it is possible that it came into existence with time itself on Avalon, as a sort of safety valve for the Time Stream.  At some point in its origins, the Gate was bound to the Phoenix by some unknown person or entity, who was also the first to understand how to use it. 
The Gate appears next in 975, when Princess Elena's father made it her dowry for her marriage to Prince Malcolm. The Archmage learned of this, and was aware (as Elena and her father presumably were not) of its true nature; desirous of obtaining it so that he could combine it with the Grimorum Arcanorum and the Eye of Odin to become an all-powerful sorcerer, he sent bandits to seize it from the princess and her escort, the Norman Ambassador. The bandits were foiled by the time-traveling Xanatos, Fox, and Petros Xanatos, arriving from 1995 with a future version of the Gate. The Archmage next sent Demona, then his apprentice, to steal the Gate, but she encountered both her future self and a future Goliath, beheld the aftermath of the Wyvern Massacre nineteen years later, and decided to tell the Archmage she had lost it instead of yielding it. She split the Gate, sharing half with Goliath as a token of their love. ("Vows")
Both kept their halves over the next 1020 years, until Xanatos and Fox's wedding in 1995. Xanatos and Demona tricked Goliath into attending the wedding with his half so that Demona could reconstitute the Gate and travel to 975—Xanatos to arrange for his financial future, and Demona to attempt to persuade her younger self not to share the Gate. Upon returning to 1995, Goliath stores the Gate at the clock tower with the Grimorum and the Eye of Odin. ("Vows")
Under the Weird Sisters' instructions, Demona and Macbeth stole the three magical objects from the clock tower and delivered them to the Archmage. ("High Noon") The Archmage would use the Phoenix Gate to go back in time and rescue himself from the abyss in 984 and bring his younger self forward in time, helping him set up the steps that he would need to become the "enhanced Archmage." When Goliath finally defeated the Archmage, struggling with him across multiple time periods, he took the Gate into his custody to make certain that it would never be used again. ("Avalon Part Two" & "Avalon Part Three") 
However, he broke that promise when the Avalon World Tour came to London and he encountered Leo and Una, who blamed him for their friend Griff's disappearance in 1940 and kidnapped Elisa, Angela, and Bronx in retaliation. Goliath chose to use the Gate to go back to 1940 and learn what happened, in the process meeting the three gargoyles and "saving" Griff by bringing him forward to 1995. ("M.I.A.")
Near the end of the Avalon World Tour, Puck attempted to trick Goliath into giving him the Gate so he could bribe Oberon into letting him avoid the Gathering. He caused Goliath to experience a vision of a grim and bleak New York in 2036, ruled by Xanatos, with the only way of saving the city to use the Gate to change history. Discovering Puck's ruse and that the Gate needs to be "forked over" for Puck to acquire it, Goliath activated the Gate and threw it into the timestream "without a mind to control it," hoping it would be lost forever. ("Future Tense")
But Goliath was wrong. In early 1997, the Phoenix Gate reappeared in New York, in front of Brooklyn, Angela, and Broadway while out on patrol. When Brooklyn tried to touch it, the Gate disintegrated, releasing a great fiery bird—the Phoenix—which spirited Brooklyn away to 997, in front of a horrified Broadway and Angela. ("The Gate") The Phoenix then proceeded to transport Brooklyn to various other parts of the timeline for the next forty years of his life, finally returning him to Manhattan forty seconds after he had left—with his new family. We do not as yet know what became of the Phoenix afterwards, though there has been some indication that it returns to its starting point in time and begins the cycle anew. ("Phoenix") 
In order to activate the Phoenix Gate, one must hold it and speak the Latin incantation, Deslagrate muri tempi et intervalia! (which roughly translates to "Burn down the walls of space and time!").  Afterwards, a ball of fire will appear and teleport the speaker and anyone close enough to him or her to whatever time and place on Earth the speaker had envisioned.  The ball of fire vanishes once the Gate itself travels through the vortex.  The one known exception was the "enhanced Archmage," who could control the Gate without even a single spoken word, presumably through sheer will.
Time travelers in the Gargoyles Universe, whether using the Phoenix Gate or any other method (no others have yet been discovered), are unable to change history, for the simple reason that they have already been to the past. Thus, Xanatos' trip to 975, the Archmage's trip to 984, and Goliath's trip to 1940, were all events that could not change the past, but merely served as part of it; Xanatos' visit to Castle Wyvern in the 10th century brought about his receiving the rare coin in 1975 that he had already received twenty years before he left, and similarly Goliath's time travel adventure became responsible for the very disappearance of Griff that he had gone to 1940 to investigate. On the other hand, Goliath was unable to return Griff to the London Clan's shop during World War II, and both Demona and Goliath failed to alter the pattern of Demona's behavior from 975 onwards, although they both made the attempt. History is immutable; the very attempts to change it become part of the already-existing pattern - were part of it all along.
While the Phoenix Gate is said to have been forged on Avalon, it is clearly an example of "mixing magics" due to the Latin incantation required to use it. The reason for this is believed to be so that mortals can harness the Gate, though it should still be considered fairly dangerous. 
References In Other Media
In the "Young Justice: Phantoms" episode, “Nomed Esir!”, the Phoenix Gate (along with the Grimorum Arcanorum and the Eye of Odin) makes an appearance in Jason Blood's collection of magical artifacts. He insists that Mary Marvel not touch it.