Most BI tools are used for data analysis/discovery/exploration/etc. Lots of charts, lots of tables, lots of filters, loads of KPIs, off you go.
This is how most of us sift through data sets to find connections and insights. But what do you do once you have found something insightful? When you have a story to share. It is time to transition from data analysis-styled applications into more of a curated knowledge presentation of the data.
Less is More
The aphorism "Less is more" by celebrated German architect and design visionary Ludwig Mies van der Rohe is about taking a restrained approach to design. Using less decorations, less "stuff", creates a more useful more powerful design.
Curated knowledge is when a curator has done the research for us and presents us with the most relevant and useful information. It is the distillation of lots of information into something more focused and concentrated. It isn't up to the audience to find something interesting in the data - the author is explicitly sharing the most interesting things with the audience. There is a narrative and the graphics are there to support that.
This is the mindset of how to design for sharing insights in data. Focus on simplicity, remove the extraneous filters, charts, and KPIs. Show only what is absolutely essential to tell the story.
The New York Times regularly does this really well on the Upshot. They have a story to tell and the charts are an integral part of that story. The charts can be interactive, sometimes with some slight filtering, but just enough to still stay on point. Nobody wants to get lost in a quagmire of extraneous filters that ultimately don't help to understand the story.
It pains me to say this, but most people don't care about your app as much as you do. People have other things to do. When you are sharing curated knowledge with others you need to get to the point as fast as possible. You shouldn't use the app you used to explore the data to present the data. If they want to explore more you can always share with them the app you used to do your initial data analysis.
So whether you are embedding charts in a blog or giving a presentation, stay focused on simplicity. Show the charts and the numbers that tell the story. Use the charts to move your audience through the story to drive home the result of your data analysis.