The actual screen representation of a jpeg file (or any other graphic file) is different from the one which lies in the file.
Because JPEG is a lossy compression, the JPEG cannot be converted BACK to the original bitmap (the one which was saved by camera and/or another program). It is converted to one (or more) new bitmap(s) which can be (and is) dependent on the program and/or operating system and/or output device (screen, printer etc.) internals.
Again, because is a lossy compression, the expanded bitmap(s) is quite bigger than the actual JPEG file. Also, as I keep mentioning there can be more bitmaps for caching, undo etc. That's why there are optimizations in place, including keeping the actual image in a compressed format (usually losseless, of course) and preparing (converting, uncompressing, painting etc.) for the screen only the part (a crop) of the image which is actually shown.
However the memory consumption isn't of a concern nowadays for the regular user, the usual bottleneck being storage read/write time and, of course, the time spent within the processing algorithms.
Related to the internal conversions between JPEG and internal bitmap(s), is important to know which are the editing actions which require this load->conversion->save process and which are the editing actions which can be done directly in/on JPEG file. This is because of the lossy nature of JPEG compression which at each conversion degrades the quality of the image.
There are programs which do all the editing actions in a destructive load > conversion > save cycle. (eg. Photoshop, Corel PhotoPaint etc.).
There are other programs which do some actions directly on JPEG file like Loseless rotate in 90 degree increments, metadata/catalog management (XMP, IPTC, Rating, Coloring etc.). All the other advanced editing actions are done via a normal load > conversion > save cycle. Usually these are the organizers, multimedia managers/viewers - personally I use XnView MP but I know that also FastStone Viewer or others has such functions.
Also, there are other programs which support a reduced set of editing actions which - regardless of the file type - apply these actions in a non-destructive manner. In fact these programs (eg. Lightroom, AfterShotPro etc.) save only the script (history) of the actions which apply each time when (a part of) the image is rendered on the screen. It needs CPU power (sometimes a lot) but one can accept this for obvious reasons. For these programs, in order to actually 'see' your edited JPG in another program you need to 'export'/'burn'/'render' it to another/same file. IOW to apply the edits to the image.