What makes Java EE scalable is what makes anything scalable: separation of concerns. As your processing or IO needs increase, you can add new hardware and redistribute the load semi-transparently (mostly transparent to the app, obviously less so to the configuration monkeys) because the separated, isolated concerns don't know or care if they're on the same physical hardware or on different processors in a cluster.

You can make scalable applications in any language or execution platform. (Yes, even COBOL on ancient System 370 mainframes.) What application frameworks like Java EE (and others, naturally -- Java EE is hardly unique in this regard!) give you is the ability to easily (relatively speaking) do this by doing much of the heavy lifting for you.

When my web app uses, say, an EJB to perform some business logic, that EJB may be on the same CPU core, on a different core in the same CPU, on a different CPU entirely or, in extreme cases, perhaps even across the planet. I don't know and, for the most part, provided the performance is there, I don't care. Similarly when I send a message out on the message bus to get handled, I don't know nor do I care where that message goes, which component does the processing and where that processing takes place, again as long as the performance falls within my needs. That's all for the configuration monkeys to work out. The technology permits this and the tools are in place to assess what pieces have to go where to get acceptable performance as the system scales up in size.

Now when I try and hand roll all of this, I start with the problems right away. If I don't think about all the proxying and scheduling and distribution and such in advance, when my app expands beyond the bounds of a single machine's handling I now have major rewrites in place as I shift some of the application to another box. And then each time my capacities grow I have to do this again and again.

If I do think about all of this in advance, I'm writing a whole lot of boilerplate code for each application that does minor variations of all the same things. I can code things in a scalable way, but do I want to do this every. damned. time. I write an app?

So what Java EE (and other frameworks) bring to the table is pre-written boilerplate for the common requirements of making scalable applications. Writing my apps to these doesn't guarantee they'd be scalable, of course, but the frameworks make writing said scalable apps a whole lot easier.