Let me try to explain it in layman terms (not that it is really difficult, it is just confusing for people that it is starting).
themehax is just a entry point, or to say it is something that "allows homebrew". The homebrew that it runs by default is Homebrew Launcher. Homebrew Launcher is the boot.3dsx file that you have in the root of your SD card. You can substitute this homebrew with any other homebrew (compatible with Ninjhax 2.x, that is the current version of Ninjhax), just swapping this boot.3dsx file with another.
HBL-emergency is one of those homebrews that you can use to substitute boot.3dsx. It is actually a simplified version of Homebrew Launcher, so it allows you to autoboot: this means that HBL-emergency is just a homebrew that loads another homebrew, automatically.
Now, why would you do that? Wouldn't it be simple to just use Homebrew Launcher? Well, it is because with HBL-emergency you can press a button, say R, to boot another homebrew that is not the default. So you could, for example, load the traditional Homebrew Launcher without pressing anything, and one mod of Homebrew Launcher (like from
mashers) pressing R.
The only thing is, remember that themehax is a entry point? Well, you're using themehax non-autoboot version it seens, so it means that the entry point is only executed when you press L while turning on 3DS. So even using HBL-emergency, you need to hold L while turning on the 3DS to load
the entry point. After the glitchy screen and the debug screen (where it shows some strange text) the entry point finished the loading and will start to load the boot.3dsx file in the root of your SD card.
At this time you may release the L button and press any other button, so HBL-emergency will get its input to select your desired .3dsx file.