Two parties A and B try to communicate with the following encryption scheme: both sides agree on the same long random bit sequence (you may assume one of your own choice). When A want to send B an k-bit message, it takes k bits from the long random sequence, XOR each bit of the k bit message with them, and send the result ("encrypted message"). When B receives the encrypted message, it takes k bits from her own copy of long random sequence, and XOR each bit of the k bit encrypted message to get back the original message.
The two parties are concerned with the possibility that a middleman which perform the message transfer will take the encrypted message sent by A and change it, before forwarding the message to B; and B will get the message without knowing that it is modified. So they add the following "protection":
Append the CRC to the original message, before encrypting the whole message (original message + CRC) using the above method (n-bit XOR). When B gets the encrypted message, it is decrypted, and then CRC is checked.
If the CRC is incorrect, B concludes that the message is modified, and ignores it.