A dual-MOBI is the default output for Amazon's "KindleGen" converter (used when publishing ebooks on Amazon).
It is also an option in calibre's MOBI Output conversion settings. (You can create an old|new|both MOBI.)
What it means is that the *.mobi file contains both the legacy MOBI content and the newer AZW3 content in one file.
Amazon's PDOC service (and publisher intake channels) only accepts dual-MOBI or old MOBI -- they don't accept pure AZW3 because that means the K1/2/DX and non-updated K3s won't be able to read the book since they only read MOBI.
...
Assuming the uploaded ebook had a cover inside it, and calibre will automatically insert the calibre cover image when converting
even if the original file didn't set a cover 
then uploading a plain old MOBI *should* show a cover thumbnail.
I just noticed your profile says you have an Android smartphone and are "considering" getting an E-Ink device.
But I am pretty sure that Kindle for Android works the same way.
Although it absolutely does matter whether you upload to Amazon's PDOC cloud or sideload with calibre -- see this calibre FAQ entry:
http://manual.calibre-ebook.com/faq....droid-ipad-etc