The Jupyter web page is a fine example of reverse information distribution. I went from" I think I know what this is" to "I have no idea what this is" within seconds of the page loading.
Same here! all of the buzz around iPython, and there is no succinct explanation of wtf it is or why I would want it. Jupyter seems to be a more generalize version of iPython with pluggable engines, but again, what does that mean?
So far, I am coming to the conclusion that iPython is a tool for data scientists, but I am not really sure.
IPython itself is a REPL with many, many convenience and magic functions, auto-completion, etc... If you write any amount of python, it's hugely useful!
Then, there are IPython Notebooks, which give you the HTML, cell-based frontend for executing code.
Jupyter is the v2/generalization for both of these things - there is the Jupyter shell, which is a plugin-friendly REPL, and Jupyter notebooks, which allow you to run code across a variety of langauges. AFAIK so far, you can only run one language per Jupyter notebook (though having dug around the source code, the possibility for multiple languages on a per-cell basis is very much there).
I still find myself using IPython and Jupyter interchangably, which probably doesn't help the confusion.
The project is currently (this month) moving from it's previous incantation called 'IPython'* to 'Jupyter'. The website apparently hasn't catched up yet.