Dan,
Vertx is a non-opinionated toolkit/framework. As such, it does not dictate such details as to where and how data is stored. It is entirely up to you. You can push your data to a database, store data in a file, or keep the data in memory. This makes vertx no different from the vast majority of frameworks. For example, php does not dictate how to save data, nor do old-school java servlets.
With this question, I get the impression that this is your first go at developing server-side web applications. While vert.x can certainly be your first platform, the vert.x documentation does assume a bit of sophistication and prior knowledge to use vert.x. Other technology (say php) will have more tutorials on how to save and retrieve your data from a database. Fundamentally, the concepts are similar with Vert.x, but the underlying tech is different. I don't want to turn you away from Vert.x, but you might want to concurrently review some intro tutorials on php/servlets/etc.
Best,
-Adam