The galaxy in question looks a little fuzzy, but that's probably because it's so far away. A lot of the things we see from space are actually past versions of themselves because the light from the object took several years to get here. According to the video description, the light from this galaxy, blurry as it may be, took a very, very long time to get to the Hubble space telescope:
This animation shows the location of galaxy GN-z11, which is the farthest galaxy ever seen. The video begins by locating the Big Dipper, then showing the constellation Ursa Major. It then zooms into the GOODS North field of galaxies, and ends with a Hubble image of the young galaxy. GN-z11 is shown as it existed 13.4 billion years in the past, just 400 million years after the big bang, when the universe was only three percent of its present age.
This new development is record breaking and astronomers don't expect to beat it anytime soon until the launch of a new, larger observatory, the James Webb Space Telescope.