Generally, a graphic is a visual art, like a picture, chart, cartoon... Many different publishing mediums such as the internet, magazines, newspapers, and so forth, use graphics because well, people like pictures. In the classroom environment, they tell you a good writer makes a picture with the words in description, and a better writer goes beyond the picture utilizing all the senses to make the reader feel like he/she is actually experiencing what you are writing about. While this is true about good writers, nine times out of ten, if you want someone to read what you wrote, you need a picture to arouse their interest.
Page vs. Image
In the world of design software, you got two major types of files that result from it. Page vs. Image. The page is basically like a document. Some software with the purpose for publishing do not make images as much as pages you'd print the images on. It's like the newspaper itself, but on the computer. Then you got image documents, which are pictures. These images can contain words, text art, graphs, and so forth no different than a page. The main difference is how it's saved. For instance, if you use Printmaster Gold software, it will save files more like a document, and it won't be something you can upload easily onto your Facebook. Now the Paint application; however, in your Windows program can save files as an image, whether it be bitmap, jpg, etc. Then you can in turn, insert that saved image file into a document.
Image File Names
Image file names that can be uploaded to the internet with ease include jpg and png, with my personal favorite being .png because it stretches better when resized. Jpg is the most popular image type, and many digital cameras instantly upload as jpg's. Gifs are best used for small icon like images, like an internet button. There are other types of file names such as .bmp and .tif, but the JPG and the PNG are what Average Joe will probably be using.
Raster vs. Vector
This is more for advanced graphic designers, but basically vector images are lines and color, like a coloring book image with or without the color. Raster images are more like your photographs. Most logos are done using vector image software rasterizing the end result (turning a vector image into a raster image).
I am a fan of Adobe: Photoshop for raster images and Illustrator for vector. The best user guide for Adobe is from people posting things online, whether they are tutorials or troubleshooting tips, and we LOVE those people who post that information.
Photoshop can come with a pretty hefty price tag. GIMP is like Photoshop but free. Some say in some ways it's better than Photoshop, and others say it's more difficult... I've never used it.
Other software is definitely available and easily googled, but I would trade in user friendly point and click ease for something that allows more creative opportunities. Like with Photoshop, you can make a texture or photoshop brush easily, as well as add effects to just a layer or a portion of the picture. There's just so much more room for creative freedom with Photoshop or I assume GIMP... And the ONLY way to learn any program is to play with it and use it regularly. Learning how to use Photoshop is a real, marketable skill. Using a simple graphic editor where you remove red eye with the push of a button isn't a skill. Removing red eye in Photoshop is.