The Google app is beginning to group certain images automatically after you search for them. At the moment it seems that this will only happen with a small selection of image types, included in which are memes, images of quotes, and images of shoes. That being said the list is very obviously not extensive, but it's highly likely that Google will continue to expand this list and eventually any time you search for something in Google and look for images of that search using the Google app, it will start to automatically suggest if you'd like to save those groups of images.
You could just as easily download the images you like and save them to your device, but this feature allows you to more or less save those images without downloading them, thus alleviating the images taking up space on your phone's storage. What's not clear at the moment is what triggers Google to ask you if you'd like to save images to a certain group. The message prompt will pop up for some stuff but not immediately and only after you scroll a certain ways down the page of results. Yet will be completely absent for other searches even if the search of images should reside in the same group, like memes for example.
Once you've created a saved group for images, when you're back to looking at any images that pop up under that search term you can long press on any of the images which will then allow you to save that image to the collection you created. If you're rather fond of images of memes for example, you can then save things to your meme collection and make it easier to go back and find specific meme images that you may have stumbled upon in the past. When Google plans to expand what images will prompt the Google app to ask if you'd like to create a collection is uncertain, but the more you use the app chances are the more you'll run across image searches that support it.