A VP is often chosen to address a Presidential candidate's perceived weaknesses. For Hillary, here's a very recent word association study that was done with voters:
Those are some pretty strong negatives.. but if there's one Senator with any national name recognition that could help address them (aside from Bernie himself), it would probably be Elizabeth Warren. Her name is associated with fighting special interests; it is her brand, her essence.
We can also note that there is no ideological objection to Hillary among those adjectives. Voters are very comfortable with where she is ideologically, so it doesn't seem likely that a liberal VP pick is going to move that number in a negative direction very much.
There's also the chance that a two-woman ticket nudges the gender gap a bit wider. Moving it from, say, +15 to +18 or might seem small, but it'd be a nationwide effect - the tide would rise everywhere because women are distributed everywhere. And since the electorate is usually >52% female, even a
slight rise in the margin would be significant; it could be the difference between a Senate seat or a state in the red or blue column.
And finally, the other role of a VP: attack dog. And I think we know that Warren is quiiiiiite capable of getting under Trump's skin. She's demonstrated this over and over again, and his responses have been, if anything, self-destructive.
There are other picks (I'm quite torn between Warren & Kaine, myself). But Warren isn't as bad as one might think.