If a stream is no longer useful/relevant/outdated, you don't to keep seeing it. Instead you can effectively hide 1-on-1s with a former direct report or file away old private/shared streams. Whatever the case, the mechanism works pretty much the same.
Navigate to the stream that you would like to archive.
When the stream is open, you will see an icon associated with the categories you have set for your home panel in the upper right corner of the stream. Clicking on this will give you a few options including Remove from home panel
Once removed, the stream should disappear from your view
Hover over the stream in the home panel and click on the three dots at the end of the line.
Choose Remove from home panel
This method works great for mass clean-up of your home panel.
So what happens when you remove from your home panel?
The stream will then be removed from your home panel but will still exist. Once removed, this stream can still be accessed via search.
NOTE: this will only remove the stream for you, not everyone on the stream.
How to add a previously removed stream back to your home panel
First, search for the name of the stream that you would like to add
Click on the correct stream
After you've reopened the stream, click on the group icon in the stream header. Then move the stream into the group of your choice - for example, I am adding the stream back to the group "Engineering"
Once added to the group, the stream will appear back on the home panel under that group.