DOC: Minor improvements on quick start

- Add `plt.show()` to first example and explain that it may be
  omitted sometimes rather than not having it in the code and
  stating that it has to be added sometimes.
  Reason: a missing show may result in no figure popup and is
  hard to debug. An extraneous show has no effect.
- Figure creation functions:
  - de-emphasize pyplot. Stating the functions is enough here.
    We don't need to say where they come from explicitly. In
    particular we haven't explained the interface distinction yet.
    So let's be quite about that.
  - Do not mention/link backends here. That concept is far too
    advanced and not need here.
 - Some more wording changes.

galleries/users_explain/quick_start.py

@@ -28,16 +28,18 @@
 # area where points can be specified in terms of x-y coordinates (or theta-r
 # in a polar plot, x-y-z in a 3D plot, etc.).  The simplest way of
 # creating a Figure with an Axes is using `.pyplot.subplots`. We can then use
-# `.Axes.plot` to draw some data on the Axes:
+# `.Axes.plot` to draw some data on the Axes, and `~.pyplot.show` to display
+# the figure:
 
-fig, ax = plt.subplots()  # Create a figure containing a single Axes.
+fig, ax = plt.subplots()             # Create a figure containing a single Axes.
 ax.plot([1, 2, 3, 4], [1, 4, 2, 3])  # Plot some data on the Axes.
+plt.show()                           # Show the figure.
 
 # %%
 #
-# Note that to get this Figure to display, you may have to call ``plt.show()``,
-# depending on your backend.  For more details of Figures and backends, see
-# :ref:`figure-intro`.
+# Depending on the environment you are working in, ``plt.show()`` can be left
+# out. - This is for example the case with Jupyter notebooks, which
+# automatically show all figures created in a code cell.
 #
 # .. _figure_parts:
 #
@@ -53,24 +55,24 @@
 #
 # The **whole** figure.  The Figure keeps
 # track of all the child :class:`~matplotlib.axes.Axes`, a group of
-# 'special' Artists (titles, figure legends, colorbars, etc), and
+# 'special' Artists (titles, figure legends, colorbars, etc.), and
 # even nested subfigures.
 #
-# The easiest way to create a new Figure is with pyplot::
+# Typically, you'll create a new Figure through one of the following
+# functions::
 #
-#    fig = plt.figure()  # an empty figure with no Axes
-#    fig, ax = plt.subplots()  # a figure with a single Axes
+#    fig = plt.figure()             # an empty figure with no Axes
+#    fig, ax = plt.subplots()       # a figure with a single Axes
 #    fig, axs = plt.subplots(2, 2)  # a figure with a 2x2 grid of Axes
 #    # a figure with one Axes on the left, and two on the right:
 #    fig, axs = plt.subplot_mosaic([['left', 'right_top'],
 #                                   ['left', 'right_bottom']])
 #
-# It is often convenient to create the Axes together with the Figure, but you
-# can also manually add Axes later on.  Note that many
-# :ref:`Matplotlib backends <backends>` support zooming and
-# panning on figure windows.
+# `~.pyplot.subplots()` and `~.pyplot.subplot_mosaic` are convenience functions
+# that additionally create Axes objects inside the Figure, but you can also
+# manually add Axes later on.
 #
-# For more on Figures, see :ref:`figure-intro`.
+# For more on Figures, including panning and zooming, see :ref:`figure-intro`.
 #
 # :class:`~matplotlib.axes.Axes`
 # ------------------------------
@@ -85,10 +87,9 @@
 # :meth:`~matplotlib.axes.Axes.set_xlabel`), and a y-label set via
 # :meth:`~matplotlib.axes.Axes.set_ylabel`).
 #
-# The :class:`~.axes.Axes` class and its member functions are the primary
-# entry point to working with the OOP interface, and have most of the
-# plotting methods defined on them (e.g. ``ax.plot()``, shown above, uses
-# the `~.Axes.plot` method)
+# The `~.axes.Axes` methods are the primary interface for configuring
+# most parts of your plot (adding data, controlling axis scales and
+# limits, adding labels etc.).
 #
 # :class:`~matplotlib.axis.Axis`
 # ------------------------------