Custody is a commonly used term in financial services and refers to the holding and safekeeping of assets, such as dollars or gold. The notion of crypto custody is a bit more complicated, since it’s about holding users’ cryptographic keys (which you can think of as passwords that unlock crypto wallets) as opposed to holding actual money. Crypto custody is typically handled through “cold” or “hot” wallets.
Cold wallets are used to custody cryptographic keys offline in a physically secure location that can’t be accessed through the internet. Withdrawals are slower, since they’re processed manually in batch loads, but the upside is added security.
Hot wallets are used to custody cryptographic keys online, and transactions are executed automatically through secure algorithms. Because they’re connected to the internet, hot wallets are considered more vulnerable to hacks and theft than cold storage methods, and can have their value capped.