PSD - PSD stands for "Photoshop Document." This is the native file type for Photoshop. The PSD file contains all of the original file information including the various text and image layers.
EPS - EPS stands for "Encapsulated PostScript" file. An EPS file can include any number of style elements including graphics, text and photographs. Once you save the EPS file, you can incorporate the document into another design element. As an example, if you would like to send a company logo to a printer so that it can be used on corporate letterhead, the EPS file would be perfect. It will not allow the user to manipulate the original artwork, but it will allow the user to scale the image without losing image quality.