How to understand why a "Best Move" is best?

Would someone explain how I can go about understanding WHY the indicated move is best versus my mistaken move, please.  It would be a tremendous help if you could use the attached image as an example, as I do not know how to determine why 14.a4 is the best move.   And, why does a4 (over d3) refute the Bxf3??

Thank you!

the only way to see it is to play the line all the way out, not just look at the weird computer moves in isolation.  Take the position from there vs max computer, play the move and the next 10 after, see if you can follow how its better.  Sometimes its really hard to spot the advantage, and sometimes the advantage is so small normal humans (under 2000ish) won't see the reasons even played out, let alone from the original setup. 

 Best as I can tell on this one, a4 defends both the pawn and the bishop (protect each other) so the queen and/or knight can move freely.   Why it rejects BxN after a4 for black, though, I do not see it.   

Also read the computer spew with both eyes open.  D3 is a mistake (???!!!) is nonsense, you are 0.0 (perfectly matched) afterwards (in my book a mistake sets you back).  I would call it an inaccuracy (missed a chance to do better).  Its not a 'bad' move.  Your king is a little more vulnerable, but he can do that either way, BxN is what I would do as black no matter what you do, unless you find an attack. 

Your insight into a4 protecting the bishop makes perfect sense to me.  And you nailed the confusion I was having when I did try to follow the two lines a few moves ahead...that the BxN is refuted, so it becomes a new line altogether; thus, my novice eye is not keen enough to figure out why black's Q now moves instead of BxN, simply because of the a4 move.   I just wish I knew how to use the engine and analyses better to my advantage.  Nonetheless, your information was very helpful. Thank you!

you can use it to your advantage.   play it from there, play the recommended a4 and then BxN for black, and see what disadvantage you get into, or if its anything a human can see there.   I mean its the same thing I said, but all I know to do is play each move to see why its worse against maximum computer.   But sometimes, all you get from that is a score, .. no material changes hands, but instead of +1.3 your alternate line is +1.23 .. /derp that means jack all to me usually (I believe it, but I can't see it).   If its more than 1 full point, it should be human notable, and if its more than  2 points and you still can't see it, ... that I can usually spot (esp if you post the board/game so I can move around a little and not a picture). 

@jonnin  Gotcha! thanks a bunch!

Thanks!  That makes a lot of sense.

I'm trying to understand from the peanut gallery. 

Wow...that is a huge help! So much appreciated. Thank you!