A Genesis Portal is a gateway that exists within different realities and allows for traveling between them.
They were first discovered 200 years later by a scientist named Professor Von Schlemmer, who explained to Silver the Hedgehog what they were and what caused them, as well asking him to further investigate the portals.
Silver went back in time and aided Sonic in chasing The Ifrit back through a Genesis Portal that it emerged from as well as explaining the nature of the portals to the latter. Unknown to the two, Eggman was spying on them and thinking of how to use the Genesis Portals to his benefit. (FCBD 2015)
The former is aided by the arrival of Silver who has been closing further portals that have opened. Silver is able to help Sonic to claim the Emerald, as well as finding another portal to send him back home, though he and Metal Sonic end up through separate Genesis Portals. Both of which land them in different, unknown dimensions. (Sonic Universe #75)
In 21XX, Sigma learned about the Genesis Portals and how to control them, and decided to travel to Dr. Eggman's world. There, he used Orbot as a host and made the Deadly Six and Dr. Eggman work for him, forcing Eggman to create a new body for him. When Sigma moves to the new body and orders Eggman to create more for him, he complains that it is to much work for a single person. Sigma agrees and creates a Genesis Portal in front of him, pulling Dr. Wily from Mega Man's world to help. (Sonic Universe #76, Mega Man #49)
In a jungle on Bygone Island within an alternate continuum in Sonic's multiverse, Sticks the Badger comes upon a Genesis Portal with an unidentified individual emerging from it. (Sonic Boom #7) The individuals were later revealed to be Mega Man X, Zero, and Axl, who had been pursuing Sigma after he escaped through one of the Genesis Portals, based on coordinates Silver the Hedgehog supplied to them. However, it turned out to be a completely different universe from the one Sigma escaped to. Sticks then attacked them believing them to be invaders, although after learning why they were there in the first place, she then offered to help them with similar technology in her universe's equivalent of Dr. Eggman's lair. (Sonic Boom #8)