The Veil

Pay no attention to the plane behind the curtain.

The veil refers broadly to the space that separates the three planes of the universe. It serves as the support system that holds everything together. The Arcanum Circular runs through the veil, as it has to reach all three planes, and so the veil is bursting with mana, even more so than the Metaphysical Plane. However, beings can't normally survive within the veil (outside of specific circumstances such as warlocks) due to the fact that they would perish from mana inundation.
The dimensional aspect centers around manipulating the veil. Spells that allow for trans-planar travel cut through the veil to create portals; these spells are only possible due to the fact that they supplement the massive mana costs by borrowing mana directly from the veil's massive supply.

Rifts

The veil has many natural weak points that allow the planes to come into contact. These areas are called rifts. Rifts can only truly exist between the material plane and the metaphysical plane, as any rifts opened to the essential plane will close on their own due to the nature of the essential plane.
Rifts have a multitude of effects. Most importantly, they allow for cross-planar travel, though there are other effects.
On the material side of things, the local environment will start to become saturated with mana, and will start to take on the loose adherence to physical laws that can be observed in the metaphysical plane. This mana saturation also allows metaphysical beings to exist in the material plane, as long as they stay near the rift and don't linger for too long. Additionally, warlock patrons will be able to exist physically near rifts as well, except they don't have a time limit due to their bond.
Over in the metaphysical plane, areas with rifts will be uncharacteristically stable, which allows for them to be located reliably. This is due to there being a mana deficit near rifts, which can actaully make areas near rifts inhospitable.
After the Uniting Treaty was signed, the Celestial Order began monitoring naturally occurring rifts through the use of warlocks. This is Amelia and Polyhymnia's job at the start of the series.