The Trans-Dimensional Portal is a form of technology that can open dimensional barriers allowing individuals to travel from one dimension to another with relative ease. The Technodrome is equipped with a large portal in its main control room. This portal can allow individual people to travers dimensions or even move the Technodrome it's self. It was used mostly in the 1987 TV series. However, to open a portal big enough for the entire Technodrome required a great deal of power.
Usually the portal was used to travel between Dimension X and Earth, but has been used to travel to Dimension-Z, the Dimensional Limbo, the 2003 Turtles Dimension, and to Turtle Prime (The Mirage Turtles Dimension).
Donatello built a small portal that he kept in his lab in the lair. It never worked very well, but occasionally would open long enough for them to get to and from Dimension-X.
During the Turtles Forever special the 1987 Donatello and the 2003 Donatello built a trans-dimensional portal stick from the parts of a flash light. This allowed them to travel to the 1987 Dimension, the 2003 Dimension, and to Turtle Prime.
The Technodrome was completely redesigned by Chr'ell Shredder during Turtles Forever. That included the Portal room, making it capable of analyzing the two teams of Turtles in order to locate Turtle Prime.
Krang created a small portal in the Hall of Science building when he and Shredder had to make a temporary base there. This new portal allowed them to finally return to the Technodrome and begin a plan to finally defeat the Turtles.
Donatello and Michelangelo traveled to Dimension-X in the final episode of the 1987 series. The Technodrome had been long abandoned and severely damaged by this time. They used the Technodrome's portal to return home, but it barely had enough power to operate.
In the 2012 TV series, the Kraang use a similar Transdimensional Portal to travel to Earth from Dimension X. The portal is first mentioned in "It Came From The Depths", and first shown in "TCRI". This portal is located on the top levels of the main TCRI building. Leatherhead was able to sabotage the portal by stealing and hiding the power cell that fueled it. He later entrusted the power cell to the Turtles, but the Kraang eventually stole it back and got the portal working again. When the Turtles and Leatherhead broke into TCRI to destroy the portal, they were unable to stop the Kraang from using it to bring Traag to Earth. In the end, Leatherhead was forced to pull Traag back through the portal with him to prevent anything else from coming through, and the Turtles were forced to escape TCRI before they could destroy the portal. The design of the portal vaguely mimics the Utrom Transmat.