A burner wallet is what most players will use to play Dark Forest. It is a wallet, like any other Ethereum wallet, but it's meant to not be used for a lengthy period of time or with a lot of funds. It is meant to be temporary, and eventually discarded - hence the name burner.
When a player goes through the process of setting up a Dark Forest account, they are prompted to either create a burner wallet or import a private key.
Creating a burner wallet
Creating a burner wallet will create a new Ethereum/xDai wallet with a public key and a private key. This key is then stored within the browser's localstorage, which is generally NOT SECURE.
Importing a private key
Importing a private key allows a player to import a private key from another Ethereum/xDai wallet that they already control. Importing a private key also stores that private key in the browser's localstorage, therefore putting this wallet in an insecure position as well.
Regardless of the method chosen above, the private key for that wallet will be stored in the browser's localstorage. This is NOT SECURE, because if the server was compromised or if the browser was compromised or any other plethora of security compromises occurred, the private key would then be easily accessible.
If the private key is accessible, this means all the funds on that wallet are accessible and the Dark Forest account attached to that private key is accessible.
For these reasons, regardless of creating a new burner wallet or importing a private key, the wallet that is used for Dark Forest should not be sent more funds than necessary to play Dark Forest.
After going through this step, a player is then prompted to input their whitelist key to continue the process of setting up a Dark Forest account.