The game has multiple elements that make it appealing. For one, there is only one solution to the puzzle; you either get it or don't. It also has a high chance of success. I have yet to fail at a word in the main game; however, my pass rate at the older puzzles is only about 95% ("Jaunty," Delta," and "Gamma" were some of my losses). It also only deals in five letter words, even if some of them, such as "moult," take their spelling from outside the United States (as the game was created in the United Kingdom).
The game has a clean and comforting aesthetic. If a letter is in a green box, that means it's in the correct place. If it's in yellow, the letter is somewhere in the word. Grey boxes hold the letters that are not used in the word. This makes the game more of a puzzle game than just a word-guessing game. Personally, I wouldn't mind a box color that could indicate that a letter was used twice.
One of the best things about the game is that everyone around the world has the same word (and only one word) every day. This is why people are posting those strange pictures of blocks. The game is set up to let you share how well you did on a particular word (as well as overall progression). There's something comforting about seeing that your friends also struggled with a particular word--and something deeply satisfying about seeing that you did much better than them.
In my opinion, it's a great way to start the morning.