Cold Storage refers to the storage of reserved cryptocurrency away from the internet to keep it safe from hacking or theft.
Keeping cryptocurrency or tokens in cold storage greatly increases the security of any cryptocurrency storage scheme. This is because if any machine holding your cryptocurrency is disconnected from the internet, the chances that a hacker might get access to your cryptocurrency holdings are greatly reduced since hackers cannot penetrate into systems that do not have an internet connection.
An example of this is using a hardware wallet to store Ethereum or Bitcoin. Other methods include using a paper wallet, or by purposely keeping a computer holding the currency away from the internet.
Keeping tokens in an exchange does not constitute cold storage even though most exchanges keep a reserve of tokens in cold storage which is only accessed when extra liquidity is required.
It is highly recommended that cryptocurrency tokens that are not being used for your daily needs like purchasing or trading be kept in cold storage to minimize risk of theft.
Proper safekeeping of coins in cold storage also means storing the computer, mobile device, hardware wallet, or paper wallet in a physically secure place, this is to prevent thieves from physically taking your hardware wallet, computer, mobile device or paper wallet from you.