What is a test cycle and why it is important to carry out testing in cycles?

A test cycle is an execution of the test process on a particular build of the test object.

Usually test execution happens in at least 2 cycle. Typically in each cycle, all the test cases will be executed to identify any blocking, critical defects, and most of the high defects.
The goal of the second cycle is to identify remaining high and medium defects, correct gaps in the scripts and obtain results.