What does a GM’s “second” really do?

Well, even Walter White needs help from Jesse. 

On gameday? Moral support...

When I was in High School, I asked the track coach what he did- I mean how much coaching can you do in track? Run as fast as you can from here to there...

Ends up, there is a lot to do ahead of time to get the maximum performance out of a runner- things like creating exercise, practice, and nutrition plans, training optimum performance out of the starting blocks, and developing a pace plan for each runner in each race. 

So yes, on game day he says play chess good and holds coats.

Analyses opening lines and looks at their opponents past games e.t.c

A stunt double perhaps? 

Nowadays the seconds probably help with preparation.  In the old days, when games were adjourned after 40 moves, the seconds would assist in analyzing the position for the resumption of the game the next day.

Lets say you're Fabi and want to play the petroff (or any opening) in a world championship. You're going to want it to be cutting edge. So first of all you have to look at all the petroff games played that year at a minimum. You have to look at all the games Carlsen has played against the petroff. You're going to want 100s of hours of human guided engine analysis looking for new ideas and the lines Carlsen may have prepared against those new ideas etc. That's just one opening.

In other words there's a lot of work to do so they have help. The seconds do the grunt work (or a lot of it), and hand off a finished product (or nearly finished) to Caruana. Like research assistants.

When Bobby Fischer was asked why he didn't like having seconds, he said that he didn't want to be giving chess lessons for free.

Later on (right before the 1972 match) he had a second who would bring him coffee and play tennis with him.

Common task of seconds is opening preparation, finding a way how to break the opponent by digging deep in the database and by use of engines.