Dotted Slurs?

[Walrus]

I'm not exactly new to music, but there are still some high-level markings that I don't know, such as a dotted slur line. When I first saw it, I looked it up, and figured it meant "no breath," which made sense because all I had seen so far was the slur over a bar line between a quarter note and eighth note.

Then I saw it over a set of 4 sixteenth notes, and obviously I'm not going to breath between each note there, so a "no breath" mark seemed irrelevant.

So what is this strange dotted slur that I've never seen before?