Photoshop is primarily a bitmap image editing program. Bitmap means that the number of pixels are fixed within a certain image. These pixels can be duplicated, destroyed, and changed in many ways but whenever you do this you alter the original look of the picture in some way. This especially becomes obvious if you try to enlarge a picture. Say you enlarge a 100 px by 100 px 72 dpi image to 200 px by 200 px. You will indeed get a bigger picture but it will sacrifice image quality. The enlargement simply doubled the pixels from the smaller image, resulting in a bigger, yet blurred and blocky picture.
Vectors on the other hand are special outlines which can be created within Photoshop with the Pen, Shape, or Type Tools. Vectors differ from bitmaps because they are represented by lines which can be enlarged and shrunk without losing the image quality along the vector path. This is done by changing the actual mathmatical calculation by which the line is represented. Any change of the image size results in a nice, smooth line every time.