What is meant if a wallet is cold or hot?

TL;DR: A hot wallet is a Bitcoin wallet connected to the internet, while a cold wallet is not. In general, hot wallets offer more convenience for day-to-day spending but are less secure because they can be targeted by malware from the internet. In comparison, cold wallets are deemed safer for storing large amounts of bitcoin since they are not continuously exposed to the internet.

The distinction between hold and cold depends mainly on the preparation required in order to spend bitcoin from a wallet. This is closely related to the degree to which a wallet is online, i.e., directly or indirectly connected to the internet.

When a wallet is connected to the internet, it can sign transactions and send your bitcoin immediately. We call this a hot wallet. However, an internet connection also makes it vulnerable to possible security compromises like remote access.

On the other hand, a cold wallet is not connected to the internet and is mainly used for generating and storing private keys offline. If you want to send bitcoin from your cold wallet, it requires manual action, such as connecting a signing device (hardware wallet) to a Bitcoin node to sign.

There are also more categories than hot and cold, such as a warm wallet, where the signing device is connected but requires user interaction to sign. Note that such wallets can still be exploited, e.g., by a thief, but not by a remote hacking operation via the internet.