The field of view is tiny: if you wanted to cover the whole sky with a grid of similar images you would have to make 16 million of them! It would not be very practical because the Hubble Space Telescope (HST) had enough trouble taking this one picture. It took it about a month of accumulated gazing at one spot in the sky to obtain just one image. Not in a million years (literally) could the HST cover the whole sky with such images!
What was the point in having one of the world's most famous and most expensive scientific instruments dedicate so much of its time to a single spot in the sky? What is more, this particular spot was chosen because there it is particularly dim and dark, not containing any stars except for a handful of very very very faint ones. What made it worth staring at for so long? What were we expecting to see there?
We wanted to see as far into the distance as we could and, since light takes time to reach us, as far into the past as we could. (Note, of course, that we are seeing the light the stars are making and sending to us; we are not shining light on them! This means, of course, that we can only see those things that shine brightly enough for us to detect them. It also means that we can only see them as they were when that light left them; we can never know for certain what those galaxies look like "now"... or indeed if we can even talk about them and us sharing the same "now.")
Since we depend on the light these objects emit, we need a very sensitive camera to detect that light. If a lot of light reaches such a camera, you only need a very short exposure time to take a picture; but when there is less light, you need longer exposure time. And the farther away a given light source is located, the fainter it appears to our camera. Therefore, taking a picture of the most distant (and therefore oldest) objects in the Universe requires a very long exposure time... and a field of view with no nearby bright stars to blot out the fainter distant galaxies.
Within the XDF image one can find a handful of stars from our own Milky Way galaxy, like specks on a window through which we are looking; but mostly what we see are a staggering 5,500 little fuzzy blobs of light. Every little smudge in the picture is an entire galaxy, each comprising hundreds of billions of stars!
The oldest galaxies in the picture are 13.2 billion years old, i.e., some are shown as they were only a short time after the Big Bang (which was 13.7 billion years ago). In five years or so, with a bit of luck and a lot of dedication, HST's successor, the James Webb Space Telescope (JWST) will be built and placed in its designated orbit around the Sun. One of its projects will be to take a picture of even fainter objects - fainter and therefore farther and older - the very first stars that ever existed...