While this new mode is a spectacular addition to the iPhone 7 Plus, it's not to be compared with true bokeh taken taken with a large aperture and decent focal length on a DSLR. There's a lot of software magic going on here to simulate the effect, and it often results in softened edges on your subject and ignored gaps, though it fares much better on actual people and animals than inanimate objects.
It's still in its beta phase, so it's likely to work better when it hits the masses. Right now, it's fairly intuitive, and tells you what you're doing wrong directly on the screen so you can reposition or get more light.
However, it automatically takes two pictures every time you take one in Portrait mode—a regular photo and a "Depth Effect" version—and that can eat up space real quick, as well as double the clutter on your iPhone (and eventually your computer).
HDR has always done this, and the process for disabling it is exactly the same. Just go to Settings -> Photos & Camera, then scroll down and toggle off Keep Normal Photo. If you ever decide that you'd like to keep originals later, just go back in and toggle it on, which might actually be a good idea since there's still some bugs that need worked out in Portrait mode.
Don't think this is a big deal? Well, as an example, the regular version of one photo could be 5 MB in size, while the bokeh effect could trim that down to about 3 MB in size. So if you take 500 photos in Portrait mode in those sizes, you'd have sucked up 2.5 GB of space just from the regular images alone. That's a total of 4 GB of space used up in total, versus just 1.5 GB if you kept the bokeh ones only.
If you've got a 128 or 256 GB iPhone 7 Plus, you probably don't care. But if you have the 32 GB model (which is really only like 27 GB of actual space), you'll have to keep your Photos app tidy.