This video pans around "slices" of the Universe at different times throughout its history (present day, and at 4 and 11 billion years ago). Each slice goes further back in time, showing how galaxies of each type appear. The shape is that of the Hubble tuning fork diagram, which describes and separates galaxies according to their morphology into spiral (S), elliptical (E), and lenticular (S0) galaxies. On the left of this diagram are the ellipticals, with lenticulars in the middle, and the spirals branching out on the right side. The spirals on the bottom branch have bars cutting through their centres.
The present-day Universe shows big, fully formed and intricate galaxy shapes. As we go further back in time, they become smaller and less mature, as these galaxies are still in the process of forming.
This video is illustrative. The Hubble images of nearby and distant galaxies used were selected based on their appearance; their individual distances are only approximate.