You can play and enjoy the game by just using the decks you bought. Buying booster packs that you saw with extra cards is like jumping down a rabbit hole. The more cards you buy, the better decks you can build, but the more cards you want to continue building better decks.
A booster pack contains 10 random cards from that particular set (5 common, 3 uncommon, 1 rare, and 1 holo). The boosters could be any type of cards, that you may or may not want. With the decks you have now, you have a fairy deck and a dark deck. So if you bought boosters for extra cards you'd be looking for cards that would benefit those.
Whether you buy boosters or not depends on how you want to play the game. If your two boys are still quite young it might be easier to stick with the theme decks because they're very basic and easy to play, and quite slow paced. If you're looking for a more exciting/diverse gameplay then buying boosters would be very beneficial because then you can get into having decks that you can run through quickly to get the cards you want, cards to mess with your opponent, multiple strategies, etc. It all depends how you want to play the game, and especially how much you're willing to invest into it. Keeping up with high level cards gets VERY expensive.
Playing online is a bit different. Every pokemon deck or pack comes with a code to play with online. The decks give you that deck online, the boosters give you a code for a booster from that set (but you'll receive different cards when opening the online booster pack than you got in real life).
The online game is great because you can randomly get matched up against someone online, so you always have someone to play against. It's also much easier to get more cards.
In the online game there's the "Trainer Challenge" which is basically just playing computer AI over and over, but by completing that you get about 45 free booster packs, which is 450 EXTRA cards for free. That's always a really good start to building some great decks.
Also by playing online against random people, and in the online tournaments, you earn free booster packs as well as tokens which can be used to purchase more packs! So although it isn't quick, you can earn many many free booster packs just by playing in the online game.
Me personally I have thousands and thousands of cards, but have stopped buying them. It was just way too expensive to keep up with the cards, so I switched over exclusively to playing the online version. I can earn boosters quickly, and over on /r/pkmntcgtrades you can buy online pack codes from fellow redditors for pennies. In stores a physical booster pack is at least $4, you can buy online packs for about $0.20-0.40. That's why I switched, it's cheaper and more convenient cause I can play it on my iPad wherever I go.
Sorry if that was a lot to read, but if you have more questions feel free to ask. Also, if you ARE looking to get more into the strategies and deck building, feel free to ask, we have lots of input on that around here :)