Oscilloscope: trigger and multiple periods of the signal
Once triggered the trace runs to completion (at whatever speed you set the timebase to). Any trigger events occurring during the trace are ignored. After a trace has completed the next trigger event that occurs will start the next trace.

The trigger is used to not overlap the successive traces of the signal
on the screen.

Overlap can be interpreted in somewhat different ways. In this case we use the trigger so that each successive trace is drawn in the same place as its predecessor. So if we have a stable input signal we see an apparently static trace on the scope, even though it's actually being continuously redrawn from different samples of the input signal.