If you want to create graphics for your web page you'll need some form of graphics software. Depending on the graphic you need to create, you will need either illustration software or image manipulation software, or both.
Image Manipulation Software
An image manipulation program (also referred to as a "photo editor"), is normally used to modify existing images. It can also be used to create images, but there are some types of images that are much easier to create using illustration software. Image manipulation software is perfect for touching up and resizing photos.
Adobe Photoshop and PaintShop Pro are two other leading photo editors.
Illustration software is normally used for creating illustration style images. Examples include logos, icons, decorative images, and illustrations.
Adobe Illustrator is a leading illustration package used by professional design studios around the world. Xara Xtreme is another popular package.
If you don't have the money to pay for a program like Illustrator or Xara Xtreme, try DrawPlus by FreeSerifSoftware. DrawPlus is free as long as its for your own personal use.
Vector versus Pixel Based Software
Probably the biggest difference between illustration software and photo editing software is that one is vector based and the other is pixel based.
Illustration software is vector based. Without going into the technical details, one benefit you get from this is that you can scale your images up without the image deteriorating. With pixel based images, if you increase the size of the image, it gets all "pixelated". You may have seen this happen occasionally with images - it becomes blurry and the lines tend to look quite jagged.
Pixel based software (i.e. photo editors) also have their benefits. In particular, photo editors enable you to do some amazing things with photos. You can zoom right in and change colors pixel by pixel - something you can't do easily with vector based software.
You may only need to use one of the two types of graphics software. This will depend on what type of graphic you need on your website. If you only want to touch up or resize photos, download GIMP. If you want to create a logo, or some sort of illustration, download DrawPlus. If you're not sure, why not try them out anyway. That way, you'll get to see the different options that each one offers.