A wallet whose keys are held on an internet-connected system so that transactions can be signed automatically.
Why it matters
Exchanges need hot wallets to process withdrawals at speed, which means some proportion of customer assets is always exposed to remote compromise. The Coincheck and KuCoin incidents were both hot-wallet losses. The question worth asking a custodian is what proportion sits outside cold storage, and what protects it.
Not advice. Definitions are for understanding, not instruction. Nothing here is financial, legal, tax or security advice.