Verse Cores are metaspacial, trans-dimensional structures existing naturally in large numbers throughout the Omniverse. It is believed that they are "focal points" for the laws of physics, allowing groups of -verses near them to be mutually hospitable for each others' life (thus preventing the existence of Incompatible Beings).
The exact origin of the Verse Cores is unknown. It is possible, though, that Creator inserted the Cores as a means of allowing trade and communication throughout the Omniverse. The Guardians of Aleph are devoted to defending the cores, though they cannot possibly hope to defend all of them given that there are infinitely many in regions that the Guardians are unable to access.
The destruction of a Verse Core (which requires an extreme amount of firepower; only very powerful Cosmic Entities are capable of doing this) causes the collapse of shared physics in all the -verses nearby, which can be catastrophic to life, cosmology, and reality.