Is this a valid Apple request to download software? I seem to have a USB connection that's a little flaky and will address it. 

When my iPhone, connected to my MacBook made that sound it does when it is first connected a few times in rapid succession, this message appeared. 

I snapped a quick screen shot, unplugged my phone and clicked Not Now rather than Learn More, or check Activity Monitor, so I can say much more than "this is how it looked," and no matter how I wiggle the connection I can't reproduce it.

It looks vague and ominously non-Apple, for reasons I can't explain. Is this a standard thing to happen, or is it weird or even potentially dangerous?
It looks legit, but was probably shown to you by mistake, triggered by the rapid connecting and disconnecting. If you are concerned, you could run MalwareBytes Mac to make sure you have no malware. But that message looks legit to me, unless it's a perfect replica of the real message it is emulating.