The term "jaggies" refers to jagged edges created by full color pixels that do not run in perfect lines, creating the appearance of breaks.

Notice the areas I've circled:



Because you've used nothing but black for your outlining and you haven't used straight lines in that area, the "curve" of the bottle seems choppy and broken up -- as if it has small edges instead of being smooth. That's because you have jaggies there.

Compare it to this, a quick retouch of your bottle with a 2 more colors (dark and light grey) tossed in those areas to help smooth it:



This technique is called anti-aliasing, and it involves using other shades of your color to gradually shade an edge away, so that it looks smoother. It's not the only technique available, but it is a common answer to jaggies.

Another answer, such as in the tutorial you showed, is called progressive curving, and involves counting up or down in your curves -- A "perfect" curve should be made of small sections that count down as you approach the center of the curve and then count back up as you come out of the bend. You can make a curve seem even smoother by making the sections in the curve count up or down very gradually -- 4 pixels, 3 pixels, 2 pixels, etc. You can also use more sections (a bigger curve) to make it look smoother. An example of using this to help smooth your jaggies:



You'll notice the base of the potion now seems more rounded and natural, but that the teeth along the side are still pretty strong. We can combine anti-aliasing and progressive curving (and any other techniques we like) to try and get the best possible effect:



Please note, there are any number of individuals here who could do both of these techniques (and a number of others that I can't) better -- I heavily encourage you to look around and see how others deal with uneven edges. I hope that helps!

Edited by AimlessZealot - 14 September 2014 at 12:32am

Less jaggies now, but you still have one on each side of the base, and your bottle now appears to have angled faces (like twelve-sided dice) instead of being round.