Couple of my students asked me this questions. Even though the answer is simple, I am adding it here thinking the same question may come to many others who are beginners in SSIS.
In a Data Flow, SSIS pulls the data from your source into separate buffers which it manages separately down the data pipeline. In order to see the next buffer, you click the little play button in the top left hand corner which will then give you the second buffer. The number of rows displayed can be the same or different. By doing some quick math, SSIS probably generates about 2-3 buffers for you. You can easily copy and paste the data contained in each buffer by clicking the copy data button in the top right hand corner. PFB the screenshot showing the PLAY button highlighted.
Hope this helps .. Enjoy Coding !!
Roopesh Babu V