The principle of not taking the trick, but instead playing a low card in the first seat may seem strange to some. After all, why not try to make the most of what cards you have. This is what you are doing by playing second-hand low. You're saving your top cards to use later on. One of the reasons for waiting is that that you have an opponent next to you that may have stronger cards. It is also important to remember that your partner will have the final play and they may possibly hold the boss card.
Attempting to take every trick that comes your way will often cost you a point and may even get you euchred.
Here we have the dealer sitting in East seat and turns up the ace of diamonds. South seat thinks about ordering, but the idea of putting a trump in his opponents has him worried. He decides to pass. West passed as does North. The dealer picks up the ace.
South starts the hand by leading the ace of clubs. He had thought about leading the king but this would give the wrong information to his partner. West follows suit with the 9 and North plays the king of hearts. (This may not have been the best choice as there is only one card that can top it.) The maker(E) takes the trick with the king of diamonds. The bidding team has their first trick.
Now the maker(E) leads the left. South ducks and plays 2nd low with the 9. West has no trump and he plays the jack of clubs. North follows the trump lead with the queen. Now they have two tricks.
Next, the maker(E) plays the jack of spades. He's hoping his partner(W) can get this one. South knows they need the next three for a euchre and wisely throws off by playing the queen of clubs. West tries to take the trick with the king but it gets overtaken by the ace from North. The opponents have their first trick.
Now North leads back the 10 of spades. The maker(E) trumps with the ace. South knows it's now or never: time to use the right. They have two tricks in, and need one more. It seemed luck is on their side and the king is good.
Now let's say on the second lead, South overtook the left with his right. On the next lead, the maker would have trumped South's club lead for their second trick. Then if the maker had led the queen of hearts, and South ducked they would have made a point. Sure, there are other ways this hand could have played out. Still playing second-hand low helped in their quest to euchre East/West.