Ok, probably a wasted effort but I've had good success explaining things to people so I'll try, LOL
Pixel as you know is a unit of light on the screen. it's one bit, actually. One little light bulb on your screen. Think of it like those old signs made of light bulbs. the bigger the sign, the more light bulbs, unless you change the size of the bulbs, then you can cram more into the space of the sign and make the details more precise and the image finer. So if you have 6" light bulbs on a six foot sign, the graphics will be so crude you can't really do much, maybe a letter or two. If you have light bulbs the size of an LED on a six foot sign, though, you can even make them out of 3 colors crammed together into one spot and get full color and excellent detail. not quite as good as a plasma or LCD screen but for a freeway billboard it's excellent. Then you get your LCD screen. if you wereto peer at it with a magnifying glass you'd see the 3 color light bulbs it's made out of. they're very tiny. those are pixels! When your manual says your computer can do 1280x740 maximum resolution, it means that's how many of those little tricolor bulbs it has. If you were to set your resolution to a smaller number then those bulbs would gang up and several would work in tandem together.
So if you were to look at a 400x300 pixel image on a 1280x740 pixel (think pixel= one light bulb on the sign) then you'd get a pretty blocky image compared to the 1280x740 image because you'd have a bunch of pixels all teaming up and acting together as one light bulb, like having bigger bulbs making blockier images. Like the sign with huge bulbs on it.
Printers make drops of color like those lights too, only they're ink drops. really tiny ones. So if a printer does 600 dots per inch (dpi) it literally means that it can cram that many drops into a one inch long line, and that's going to affect the quality of the image it prints.
Now there's the question of what do you want to do with your picture? Do you want it to be printed for a wall, so needs a lot of detail and has to be printed on several pages to be taped together? Do you want to put it on the teeny screen of your phone? Just look at it on your monitor? Print it on photopaper? If you put it on the monitor it doesn't actually have to be very detailed unless someone's going to zoom in, but if you're going to print it big on several sheets of paper or take it to a print shop to be put on one huge sheet of paper, then you need to make it with more pixels (light bulbs, remember?).
Most of the time unless you have a special task in mind you can just leave it on the default that Art Rage starts with. but if you're going to get it printed at a shop and framed, then ask the shop to tell you the size you should create it and copy those numbers into it. If you're going to make christmas cards and want the software to move faster, cut the numbers down by 50% or even 70% when you start out.
So, think of those highway signs with all the lights being turned on and off to create messages and those dots, those are your pixels. the more you cram into a given size board,the better the picture looks, but your screen has a display limit.
Using HP touchsmart tx2 1020ao tablet laptop with stylus and multitouch screen. I love being able to draw right onto my computer! Now if Art Rage had a "fingerpaint" mode I'd really be playing!