Tied failure times, or “ties,” refers to instances when two (or more) individuals experience the health event, or are censored, at the same time. The number of ties in your data may depend on, e.g., how detailed your time variables are (exact times have a lower likelihood of ties) and what process you are modelling (relative to others, some events may have a higher likelihood of ties).
Since the outcome is often measured on a continuous scale when using Cox regression, we assume that ties are relatively rare. Tied failure times will be discussed in more detail in The Cox regression model. Survival models also have different approaches for dealing with ties; these methods are outlined in Tied failure times.