Jupyter Notebook ecosystem docs improvements (#6877)

* Add Project Jupyter info, extra context and detail to home page/index.

* Added links, minor formatting.

* Updated homepage, adapted unified messaging on notebook page.

* Updated links.

* Added minimal description to the user-documentation main page.

* Revised notebook introduction text.

* Bullet point updates.

* Fixed typo.

* Link update.

* Changed lightweight to simplified.

* Added Jupyter Desktop link.

* Added standards info/links.

* Update standards link.

* Update standards link.

* Update link.

* Added extension to markdown file link.

docs/source/index.md

@@ -1,4 +1,26 @@
-# The Jupyter Notebook
+# Jupyter Notebook Documentation
+
+Welcome to the **Jupyter Notebook** documentation site. **Jupyter Notebook**
+is a simplified notebook authoring application, and is a part of [Project
+Jupyter](https://docs.jupyter.org/en/latest/), a large umbrella project
+centered around the goal of providing tools (and [standards](https://docs.jupyter.org/en/latest/#sub-project-documentation))
+for interactive computing with [computational notebooks](https://docs.jupyter.org/en/latest/#what-is-a-notebook).
+
+A [computational notebook](https://docs.jupyter.org/en/latest/#what-is-a-notebook)
+is a shareable document that combines computer
+code, plain language descriptions, data, rich visualizations like 3D models,
+charts, graphs and figures, and interactive controls. A notebook, along with
+an editor like **Jupyter Notebook**, provides a fast interactive environment for
+prototyping and explaining code, exploring and visualizing data, and sharing
+ideas with others.
+
+**Jupyter Notebook** is a sibling to other notebook authoring applications under
+the Project Jupyter umbrella, like [JupyterLab](https://jupyterlab.readthedocs.io/en/stable/)
+and [Jupyter Desktop](https://github.com/jupyterlab/jupyterlab-desktop).
+Jupyter Notebook offers a lightweight, simplified experience compared to JupyterLab.
+
+Read more about how to use **Jupyter Notebook** on this site, in the [User
+Documentation](notebook.md).
 
 ```{image} ./_static/images/notebook-running-code.png
 

docs/source/notebook.md

@@ -4,19 +4,25 @@
 
 ## Introduction
 
-The notebook extends the console-based approach to interactive computing in
-a qualitatively new direction, providing a web-based application suitable for
-capturing the whole computation process: developing, documenting, and
-executing code, as well as communicating the results. The Jupyter notebook
-combines two components:
-
-**A web application**: a browser-based tool for interactive authoring of
-documents which combine explanatory text, mathematics, computations and their
-rich media output.
-
-**Notebook documents**: a representation of all content visible in the web
-application, including inputs and outputs of the computations, explanatory
-text, mathematics, images, and rich media representations of objects.
+**Jupyter Notebook** is a notebook authoring application, under the [Project
+Jupyter](https://docs.jupyter.org/en/latest/) umbrella. Built on the power of
+the [computational notebook format](https://docs.jupyter.org/en/latest/#what-is-a-notebook),
+**Jupyter Notebook** offers fast, interactive new ways to prototype and explain
+your code, explore and visualize your data, and share your ideas with others.
+
+Notebooks extend the console-based approach to interactive computing in a
+qualitatively new direction, providing a web-based application suitable for
+capturing the whole computation process: developing, documenting, and executing
+code, as well as communicating the results. The Jupyter notebook combines two
+components:
+
+**A web application:** A browser-based editing program for interactive authoring
+of computational notebooks which provides a fast interactive environment for prototyping and
+explaining code, exploring and visualizing data, and sharing ideas with others
+
+**Computational Notebook documents**: A shareable document that combines computer
+code, plain language descriptions, data, rich visualizations like 3D models, charts,
+mathematics, graphs and figures, and interactive controls
 
 ```{seealso}
 See the {ref}`installation guide <jupyter:install>` on how to install the

docs/source/user-documentation.md

@@ -1,5 +1,7 @@
 # User Documentation
 
+Use this page to navigate to different parts of the user documentation.
+
 ```{toctree}
 :maxdepth: 2