These are my first impressions after playing through a few levels, but I'm not as hardcore of a Fire Emblem fan as a lot of other people are due to being terrible at strategy games. My opinions on the game should probably be taken with a grain of salt.
This is Nintendo's second mobile game after Super Mario Run (they didn't develop Pokemon Go). It's effectively a scaled down version of their classic Fire Emblem strategy game series. The gameplay, though simplified, is still relatively faithful by mobile game standards, and the touchscreen controls don't ruin the game in the same way they would ruin a platformer (*cough* Mega Man Mobile *cough*). The difficulty is nowhere near as brutal as the main games often get, and from what I've played so far, each map only takes up a screen. To accommodate this, you can only have a team of four people, and there are only a handful of enemies to fight at any given time. There's also no permadeath, which will definitely be a sticking point with many hardcore fans, but I'll elaborate on it in a moment.
Worth noting is that this is a freemium title, which is enough to scare a lot of people off, but the freemium elements seem more tastefully done than one would expect. Real money can be spent to buy "orbs," the game's currency, though this can be avoided if you aren't hasty about spending the orbs the game gives you for free for completing maps and other objectives. Orbs can be used to purchase any number of things, including characters from previous FE games. This is the most likely reason for permadeath being absent: losing characters they paid real money for forever would definitely piss a lot of players off.
One major issue with the game that it shares with Super Mario Run is the requirement that the player's phone be connected to the Internet in order to play the game. The game does have microtransactions and other online features, but requiring a player to constantly be connected to play a primarily singleplayer game is still an awful idea no matter how you slice it. It's baffling that this is even a requirement considering how many smartphone games can easily be played offline.
Overall, though it's far from perfect, Fire Emblem Heroes is nonetheless an improvement over Super Mario Run in terms of capturing the essence of its respective series in a bite-sized package. It's definitely aimed at casual players more than anyone else, but it does a halfway decent job of serving its twofold purpose: to be a Nintendo-flavored time waster and to introduce newcomers to the series. Just keep in mind that you will need to be online to play it.