Navigate to your address, click on Address Actions > Show Private Key.
The private key unlocks your address and allows access to it from anywhere. For example, when paired with the address it can be used to access this address from any location and used to send tokens contained in the wallet.
That’s why it is important to keep it secure and not disclose it to anyone (unless you want them to be able to access your tokens at this address). You can think of it as of “pass phrase for the address”: while wallet pass phrase unlocks all addresses in your Counterwallet, the private key unlocks one particular address.
Note that there are different formats of private keys (such as compressed and uncompressed). Counterwallet uses compressed key WIF.