Phantasy Star Online 2 is a touchscreen-adapted version of the classic SEGA MMORPG for Android. This means, basically, that it has a simplified gameplay and is much less in-depth than the console version.
The fighting system in Phantasy Star Online 2 is quite simple: you can move your character around enemies and attack with the appropriate button. Your character will also have several different special attack buttons and can even call a friend for help while fighting.
When you're not fighting, you can do many different things in the city (although everything is done through menus). You can't physically visit the city; you can only select options from menus in the game.
Phantasy Star Online 2 is a lackluster game. The only good thing about it is a license that, despite the passing years, remains very important.