Photoshop can read and write several image file types, each of which is appropriate for different purposes.
JPEG: General purpose; allows for variable levels of file compression at the increasing expense of image quality. (A “lossy” file format.)
TIFF: A good archival file format. Supports layers. Allows for file compression using the LZW method (a “lossless” method).
PSD: Photoshop’s native file format. Supports layers, vector and shape information, text.
GIF: Works only with limited color palettes; appropriate for use on websites.
PDF: Useful if you’re sending information to someone who doesn’t have Photoshop.