Jpeg is a flat image, it does not support layers, it does not support transparency and if you save an image as a jpeg it adds artifacts to the image which lessen the quality of the image.
An artifact is the appearance of ringing, contouring, posterizing, staircase along curved edges and blockiness/chckerboarding in areas of solid colour.
These are all undesireable effects to have within an image. Everytime you save a jpg as a jpg it adds more and more artifacts to the image, reducing the quality again and again with each save.
If you open a jpg to make edits it's best to save it as a tiff or psd file, rather than a jpg. If you add text to the image, it's best to save it with the layers in tact and as a PDF.
PSD
This is a native photoshop format. IT SUPPORTS layers, it supports transparency, it supports type (although it outputs the type as raster - so back to PDF if you have type, vector shapes or vector masks).
PSD does not use any lossy compression (lossy means data is lossed when saved, so by not using lossy compression it keeps the image data intact).
PDF
Generally the only time you save as PDF is if you include Text, vectors, vector shapes, vector masks in the artwork. PDF is fully editable after saving, in photoshop, and it supports the output of vectors, types, vector masks etc.
For any other work (bitmap/raster images), a tiff or psd file is fine. If you have transparency then psd file is for you. If you don't have transparency then TIFF is just fine too. You can have transparency in a tiff but you need to create a clipping path first - so a psd file would be better suited as it negates the clipping path steps.