When you activate or manually run a pipeline, you can see what's happening. The activity tab pops open automatically, giving you information on all the running, completed, or failed runs of your pipeline. If you want to dive deeper, you can select each pipeline run to get a detailed breakdown.
Note: If you close the pipeline and come back to it later, you won't find the activity records in that bar. You'll need to go to the activity log page for all the historical data.