I'm not sure what's "nested" about it, but that's beside the point :).
Trend considerations aside, the good thing about it is that it lets you display items of different aspect ratios without cropping the images, or with minimal cropping. It's good when you expect your users to consume the content by quickly scanning the page visually, and to rely on the images for the initial identification of the required content, e.g. Google Images or Pinterest. It's also good for letting people know that there's something below the fold, since some images are only partially visible.
If you also have text on your images, like in your second example, you need to be sure that the text is secondary to the visuals - because it's very inconvenient for scanning. You don't have text rows since the labels jump up and down, and you don't have text columns because the images get in the way. So there's no way to scan, you need to locate each item "manually" before you can read it.
If you have varying height, like in your first example, you would usually use endless scrolling because it's hard to align the bottom edge of the images, and you don't want to have empty spaces at the bottom of your grid.
The regular grid view is great for presenting textual data in addition to the images, like Facebook does, because it's scan-friendly. It's also good for paging and for whenever you might have small groups of images (Facebook albums). It's easier to fill the page when you have a standard format for your images, and then the empty slots don't look as "ragged".