HEIF stands for High Efficiency File Format and have been around for quite a while. It was developed by the Moving Pictures Experts Group (MPEG). It basically shows the same image using almost half the space compared to a JPEG-equivalent.
With iPhone 7 and newer and ios 11 you have the option to shoot photos using a space saving (HEIF) or more compatible (JPEG) format.
A few days ago I received a iPhone 8 and took an image in both formats. The HEIC image is 2.6 MB and the JPEG 4.9 MB. Both sizes in metric (base ten). So almost half the size in this case. The savings in size will vary according to the image taken but takes up a lot less space.
If you want to test the size reduction I have a site that can convert your JPEG images to HEIF. The server is written in Golang and hosted on Digital Ocean. Source code of course at Github.