Images taken on mobile devices save the image orientation in their exif metadata. If the program used to view the images doesn't make use of the exif data, the images are displayed in their original orientation. Most browsers (all browsers?) don't make an image orientation correction.

Tidypics does correct the orientation on image upload. For image files uploaded with the File plugin you can try out the Image Orientation plugin (https://elgg.org/plugins/1873029; maybe better try the latest release from https://github.com/arckinteractive/image_orientation).

(If I'm not mistaken, the future Elgg 3 will come with image orientation correction already in core.)