What Nf3-e5 move mean?

I think (as White) we often play Nf3 and develop the Knight to e5 square.
If the Knight on e5 can't be chased away or exchanged,
that is to say, e5 is the outpost for the Knight,
I understand its powerfullness and the Knight must be doing a good job.

However, often I see masters' Ne5, even when it can be immediately exchanged.
For example, White plays Ne5 and Black plays Nd7xe5.
Ne5 itself LOOKS aggresive, but it has gone anymore.

So what I'd like to know ask you is what the purpose of Ne5 was, and
who is happy with the exchange?

Specifically, please see this game.

My question is about 9... Ne4 and 16... Ne4.
Here Black put his Knight on the active e4 square,
but the horse get traded away at once.

So, how can this kind of move be benefitical?
What is the plan behind it?

Sorry for my lengthy description.
Thank you for your time in advance.

Shinji

This is an opening where Black frequently plays Ne4 and the knight gets exchanged - the main reason behind the move is that he has less space, so piece trades benefit him as he will have more space for his remaining pieces.  Of course White will exchange the knight once it gets to e4, since as you said, it is quite active on that square.

>>Paul
Thank you and sorry for my obscure description,
I meant that Nf3-e5 as white move, that is to say, Nf6-e4 move as black
which is played in this game.

>>Shoop
Thank you,,, umm, so, this Ne4 which is "apparently" aggresive is, acutally,
not intended as a attacking move, but it was played to relax the position?
and the endgame skill which I'm not good at will come into the battle, right?

Thank you.
(and after posting, I realized that I was a little wrong about where to post.
Sorry.)

Well, black isn't trading all the pieces off yet - just the knight.  He wants a middlegame where he will be slightly less cramped.  Whether he wants to enter an endgame or not is another question.

1 Nf3-e5 is the reversed Alekhine. It is not very good for black. (sorry, silly and somewhat pointless joke)

Thank you for your answers, well, I've figured out that the intentions of the moves.
Recently I'm feeling that the importance of space,
when I was under 1700(on chess.com), I was just attacking with pieces and
sometimes won due to mistakes by opponents,
however, climbing the rating ladder, I began feeling the space advantage and disadvantage.
Well this post got me understand deeper. Thanks people.