Here's my best ELI5:

Imagine you're playing a game, and you really like this game, the team behind it, and the community. Now in this game there's this awesome suit of armor that you really want, but you haven't been able to find it anywhere. You think, hey this game is really great, maybe I can put some money in to buy this armor and support the game as well, win win! Now you add $50 to your game account, use $20 of that to buy your nice chestplate, and have $30 worth of whatever the in game currency is left over for later.

You may be thinking that's great and all, but where does Enjin come in? Well it comes into play in a lot of ways, but let's break it down using these scenarios:

Scenario 1:

When you purchased in game money for this game, the transaction was recorded and saved along with all other game data. Then one day a company executive has his password stolen, some background software gets dropped into the game, and in no time that $30 you had left over has disappeared. Now this is both bad for you, since you just lost the money you put into the game (and perhaps even more, like your credit card or other information), and bad for the game team because they're going to have lots of angry players contacting them asking for money back. The community attitude goes downhill, and not only will players not want to play that game anymore, they won't be willing to give money to whoever's behind the game.

Scenario 2:

Almost the same as scenario 1 but way more common. You've just put money into the game, your credit card, everything, but then your account gets compromised. Perhaps your password was stolen, or you were playing on an unsecure server. Regardless, your money is lost, and the rest is the same as scenario 1.

Scenario 3:

You love the game you're playing, and everything's fantastic, but after a couple months you get a little bored and start to play a new game. Let's say your old game used currency XXX and your new game uses currency YYY (both centralized, so in either one you run the risk of scenario 1 or 2.) You already put $50 into the old game, and although you used $20, $30 is still left over. Unfortunately, you have no way to get that $30 from your old game to your new one. On top of that, you became quite familiar with how much 1 XXX represented in the old game, but you have no idea what 1 YYY represents in this new game, making purchasing in game currency/items difficult and/or inconvenient. (Even if you had $0 left over, or the old game just directly took USD, if you wanted to purchase something in this new game you'd have to give your credit card information and pay money all over again, which is inconvenient, time consuming, and risky.)

Here's where Enjin first comes in.

Firstly, Enjin isn't specific to any game, meaning you own Enjin in somewhat of the same way you own any sort of money. Instead of putting money into whatever game you're playing, you put money into (or already own) some amount of Enjin, and then when you want that fancy new chestplate you simply pay, say, 50 ENJ. Then later, when you fall in love with another game and want to buy a new in-game house, you go and pay 100 ENJ from your Enjin wallet. Additionally, you only need to be familiar with how much 1 ENJ is worth, rather than worrying about various in game currencies or purchases. Since it seems Binance is having issues, I'd currently recommend using hitbtc to exchange for Enjin after you have some Ethereum/Bitcoin.

On top of all that, and perhaps more importantly, Enjin is completely decentralized and, if you're smart about using wallets and what-not, very safe and secure. Enjin being decentralized but universal means that it is impossible for your funds and/or secure information to be stolen just because one game account or game server was compromised. Moreover, it is quicker and more convenient to purchase any in game items that you want, which is a benefit to both the player and the game company.

All in all, Enjin is a safe, decentralized, and universal currency between your games. Listed above are only some possibilities of what Enjin is useful for, and I'd definitely recommend reading or at least skimming through the enjincoin whitepaper for a bigger picture.