Take a trick whenever you can; it's an old euchre adage that most of us are familiar with. While this may be good advice for beginners, we soon learn that by trying to take every trick we end up sacrificing points. In addition, it may even get us euchred. Experience teaches us that often the best approach is to sit back and wait. With many hands, there is at least an even chance your partner can take the trick. This is called "ducking" or "throwing off " on a trick. The primary reason for ducking a trick is to give your partner a chance to play their winning card. It's also a good opportunity to rid your hand of any unwanted cards, and may even give the other team a false sense of security.
For example, let's say the first lead is a small club and you don't hold any clubs in your hand. But you do have a low heart that will never take a trick. While you could use a trump here, playing the heart will give you a chance to rid your hand of a loser while simultaneously giving your partner the opportunity to play - and possibly win the trick. It's well worth the risk.
The dealer sits in the North position and has turned up the ace of hearts. East passes and South orders their partner to pick up the ace. Their partner(N) then discards the 9 of clubs.
East leads the king of spades. The maker(S), knowing that they need some help in making their point, throws off the 10 of clubs. West seat follows suit and North makes good use of their ace to trump the trick.
Now North, seeing that the maker(S) threw off a club on the previous trick, thinks that may have been their only club. So he leads back the queen. His assumption is correct and South does indeed take the trick using the queen of hearts.
At this point, the maker's team needs one last trick. Under most circumstances playing the king from an ace/king set would be considered improper play. However, there are times when one wants their partner to use a trump. The other advantage to leading the king is that sometimes the player on their left will let the trick go by in the hope that their partner will have the ace. As it turns out, the third seat trumps-in and takes the trick. It now makes no difference what third leads back; the point is made.
Now go back and see what would have happened if the maker(S) had trumped that first trick? It's doubtful that the bidder would have made their point.
Letting a trick go and allowing your partner to help one of the hardest concepts there is for new players to learn.