Now if you copy that here to quote someone, you'd want to replicate his formatting, whether it be bold or underlining.
Now you see, duplicating someone else's formatting is a legitimate reason for including underlining in text. That I can understand. (I could also understand your including it, it was just the 'non-standard' usage of extraneous formatting that bugged me.)
Within the text I use blue for notes and quotes simply to make them stand out in the e-book version as not part of the main story text, thus it looks nicer. For general story text I use bold, italics, indents, and quote marks for format purposes.
I can understand wanting notes or explanations to stand out, though I'd either use indents for those, or more likely, add them as footnotes at the end, so they don't detract from the story. It's more a matter of standardized formatting that's less prone to 'the latest thing this writer comes up with'.
I've used two readers and two other reader programs on my desktop - and have four different visual presentations between them. Some strip out the position on the page, some don't. Some strip out the colour, some don't. Some strip out the font size and / or italics, some don't. But none strip out all three sets of information. Thus, as long as one set gets through the reader software changes the differences are visual and reasonably appealing to the reader's eye.
OK, I'll admit, that's the best explanation yet, as it clearly states the problem and the resolution to establish why you adopted the practice.