The final output of Photoshop is based on bitmap. A bitmap based picture is represented by pixels. Because of this, when you enlarge a picture, the clarity of the picture may decrease. In other words, you may be able to figure out the pixel in a square like shape. Generally Photoshop would be preferred for editing photographic images for this reason.
On the other hand, Illustrator is based on vector images. Here, instead of pixels, you have anchor points which are redrawn even when the image size is varied. Thus, the clarity will remain same no matter how the image is rescaled. Generally, you would use Illustrator for making posters and drawing related stuff that might undergo many forms of rescaling. This goes for vector or vexel art as well.
Hope that helps.