Val, Think of your monitor, and of your digital canvas, as graph paper. Your screen is made up of tiny squares. Color on the screen is simply squares that are filled in (more technically lit up) with a combination of red, green, and blue light. Any color in the digital spectrum can be created from those three lights. When you are painting digitally, you are instructing your computer to fill in certain squares (pixels), with the combination of light that displays the color you picked.
This jaggy effect you're seeing is inherent to low resolution bitmap images. Imagine you draw a solid diagonal line across your graph paper screen by coloring in individual squares (pixels). The line isn't smooth, it's made up of diagonally stacked squares (pixels), so the line is very jagged. That is aliased. A hard edge between filled in and blank pixels.
Anti aliasing takes some of those pixels and replaces them with lighter versions (or tinted versions, depending on what background is behind your line) that visually blend the hard edges of your bitmap pixel line into the surrounding pixels. In the case of this image, it blends black to white. The eye sees this blur, this blend, as smoothness.
Bitmap images (filetypes are .TIF, .JPG, .GIF, .PNG, and others) are pixel-based and are what is called resolution-dependent. This means that when you enlarge a bitmap, it keeps only the level of detail it had when it was created and will get blockier and blockier as you attempt to enlarge it. The pixels already in the image stay the same size. If you enlarge your artwork 200%, each filled in pixel gets 200% bigger. You can increase the resolution of an image (make the squares on your graph paper smaller, so there are more squares), but your original artwork won't suddenly have more detail. The image will just fill in the new pixels with the most logical color choice - in other words, it will do the best it can to make your image bigger using only the number of filled-in pixels you started with. This results in images that look like this:
That's why FAA says NO enlargement of bitmap images. There are programs and filters out there that do a really good job of helping your computer make these enlargement decisions, but it's not anywhere as good as just creating your image with the right resolution (number of pixels) from the get-go. For print, your canvas should be at least 7500 pixels on the long side. You can go twice that size easily. Once you start using a higher end image editing program (like Gimp or Photoshop - by the way Gimp is FREE and very powerful), you will be able to choose the size of your canvas in pixels.
Vector images are different. Vectors are lines that aren't defined by pixels but instead by math. When you draw in vector, you are telling the computer that you want to display a straight line (or a curved line) that follows along points that are defined by their location on the canvas (think of it as points on a graph). Because vector lines are based on math and not by pixels, they can be scaled up infinitely with no loss of resolution. Vectors are resolution-INdependent. They're not pixels until you tell the program (Illustrator, Corel Draw, etc) to flatten, or render, your drawing to a pixel based file type (like the types I mentioned above, JPG, Tiff, etc.) As long as they are vectors, they are simply locations connected by lines and fills. You'll notice when you look at vector art it is much cleaner looking. While vectors give you scalability, they don't offer the level of softness or blending between elements that is possible with bitmap art.
Hopefully that helps shed light on all this a little bit. The great news for you is that there are TONS of tutorials and learning resources out there for starting out with either bitmap art or vector art. Don't be intimidated! You're off to a great start on your own.
