Bitcoin Core pertains to the leading implementation of the software that gives the users the capability of interacting with the Bitcoin network.
Bitcoin Core is not owned, in any way, by any single business entity or organization. It is only updated and reviewed by the community of developers across the globe.
When Bitcoin Core is operated, the user would be able to act as a node on the network. These nodes are able to verify the validity of the blocks that are received. Transactions that were sent by other users are also verified by Bitcoin Core. What the process does is keep the coins’ miners in check, letting go of the daunting task of having to trust anyone to post the correct view of the blockchain.
A wallet is bundled into Bitcoin Core. Users are thus given the capability of using it directly from the application. Tethering external wallets to their node to validate transactions that are received are also allowed.