A Cyclic Redundancy Check involves expecting a certain property to be true about the divisibility of number of bits received.
Before the data is sent, a certain number of bits are appended onto the message to ensure that it is perfectly divisible by a given polynomial. When the data is received, it is then divided by that polynomial again, and if it does not equal then an error has been found.
It generally detects burst errors with a much higher quality than a parity check, however, it also requires sending more bits too to ensure divisibility. Additionally, integer division is a fairly slow operation for computers to execute compared to others.