At the simplest, it is a player versus player game. You are playing against peers that are getting smarter and more experienced matching yourself. This is way more meaningful than playing against computers.
A few more insights in order of skill.
Critical thinking is key. There are usually multiple ways to win. When direct damage is not going to cut it, you might have to go to plan B or C. Given your collection of cards, you can make multiple types of decks. You have to categorize all your cards and try to build a team out of them.
It teaches economics. Kids are (usually) limited by your allowance. Some cards are really good (or rare) but maybe buying 10 cheaper alternatives makes for an overall better deck. You already have certain cards, can you trade for the remaining ones? (Bartering and sales is a skill in it's own right) Can you feel that in the new season the archetype will be an aggressive deck causing this card you own to go up in price?
It involves next level thinking. Your opponent executed a seemingly unfavorable move. Is it because he has a trick up his sleeve? Or is he trying to bluff you? Is he trying to read if you have a trick? This of course varies based on skill but it is something experienced players learn (even young ones)
You have to deal in possibilities and assess your situation. You know your opponent has used x out of his 4 possible copies of this card. He has only (4-x) left in his deck of 50 so he is unlikely to draw it. Maybe the current board position is favorable for you, you are ahead in life so you should win within 4 turns. Or maybe you have 2 cards left in your whole deck that can help you win, you have yet to draw them but you need to set up the board position so that if you do draw it...
(In all card games, advantages can be distilled into two types: tempo and card. Tempo is when you are getting out ahead of an opponent in terms of board position. Card is when you have more cards in your hand. Aggressive decks sacrifices card for tempo, control sacrifices tempo for cards. Control decks chance of winning increases as the game wears on.)