Competing risks commonly occur in studies of cause-specific mortality, as all other causes of death than the one under study might happen before the individuals “have time” to die from the cause of death of interest. For example, in studies of cancer-specific mortality among cancer patients, patients may die from the cancer or from a different cause, such as a heart attack or stroke. In this case, cancer death and non-cancer death are competing risks.

The assumption of independent censoring is key to knowing how to run your analysis and how to interpret the results. This assumptions reads:

The time to the event of interest is conditionally independent of the time to other events precluding the event of interest to occur. 

This means that in the example above, there shall be no factors that influence both cancer and non-cancer mortality other than those factors that have been controlled for in the estimation.