I am surprised when Stockfish engine told me that nd5 is a blunder while suggests me to use my knight at f3 and take the pawn at e5. But, there is a black knight at c6 and if I do that, then, he will take my knight. In most strategies, it is best to exchange a weak piece for a stronger piece than for a player to exchange a strong piece for a weaker piece. It just doesn't make sense to me why. I don't know how to format the moves properly, so I've posted the link here. https://lichess.org/m21Of4sH/white The reason that I moved my knight to d5 is because in that position, my knight is centered and could prepare for an attack if needed.
Nd5 basically does nothing in this position. It spends valuable development time on a move that attacks nothing and prepares nothing; it just gives Black a free hand to start doing something meaningful (like maybe ...d6, solidifying the center and preparing to bring his other Bishop into the game at either e6 or g4). The square d5 could make a good post for a knight, but only under two conditions: either because it can stay there long term or because it can use that square to accomplish something like getting to a long-term post on a better square or support an immediate attack. Pieces are strong and outposts are good not solely because of where they are but also because they either enable you to do something or prevent your opponent from doing something. Right now neither objective is in view; and if Black really wants to evict the knight, ...Nce7 begins an immediate sequence that will either drive it away (..c6) or exchange it, whichever Black chooses. Since you have no chance at all of maintaining that outpost, why waste the time to occupy it?
The engine suggests Nxe5 because of the "fork trick," a tactical sequence (...NxN 5. d4) which destroys Black's pawn center, and typically leaves a weakly placed piece in its stead (5. ... Bd6 6. PxN BxP and if White cares at all about it a well-timed f4 will force the bishop to seek some other place of worship).
The resulting position isn't lost for Black, by any means, but it certainly leaves Black worse off than before. It's advantageous enough that I check out Nxe5 whenever I see a Black knight on c6 and bishop on c5. It's one of those tools that should be in every chess player's toolbox; a quick way to gain a small advantage without even thinking hard.
When you only have two knights developed, the only attacks that can hope to succeed are against weaknesses your opponent has created. In this case, the only weakness Black has created is the potential to decoy the knight into a pawn fork; and that's not a serious weakness -- the resulting combination does not gain material, and only slightly improves White's advantage.
FWIW, I'm not all that fond of the engine's suggested response (...Nf6). I mean it does completely eliminate any plans you might have had for the Nd5 but I'm not sure exchanging it in that way results in anything other than developing the queen early, though it does have the advantage of speed. The main thought to take away from it is this: any threat you make that can be parried easily and quickly without forcing the creation of further weaknesses is probably not worth making.
I think the idea is that after Nxe5, you have d4 which attacks both the bishop on c5 and the knight on e5. Once you take one of his pieces, you might be a little ahead on development in the opening.
Whereas if you move your knight to d5, you are moving a minor piece twice in the opening at the expense of developing your other pieces. And it won't be much useful for an attack at this stage because your opponent could easily force it back or offer an exchange. In fact, after you move d5, Stockfish suggests Nf6 and an exchange of knights, leaving your opponent's queen developed and gaining a tempo.