Core Wallet
In short: A core wallet is a crypto wallet that can contain all of the blockchain's data, not just a part of it.
A core wallet is a crypto wallet that can contain all of the blockchain's data, not just a part of it. Often called a full-node wallet, it downloads and checks every block itself; Bitcoin Core, the reference software of the Bitcoin network, is the best-known example.
Why it matters
Light wallets such as Electrum rely on external servers to tell them what is on the chain, which is convenient but means trusting those servers. A core wallet enforces the network's rules on its own, so it does not need anyone else to confirm that a payment is valid. It also helps privacy, because checking a balance never reveals the wallet's addresses to a third-party server. The cost is resources: the first synchronization can take a long time and needs plenty of disk space and bandwidth, although some core wallets offer a pruned mode that verifies everything but keeps only recent blocks.
Example
A user installs a full-node wallet on a desktop computer. On first launch it downloads every block since the genesis block and checks each one against the rules. From then on, an incoming payment appears as confirmed because the user's own copy of the chain contains it, not because a remote service reported it.