Flex nibs will actually flex the tines open with pressure as you write giving you line variation. They’ll go from an extra-fine or fine to bold or double bold line typically. With some inks this gives you a really nice shading to the lines/letters.
Normal nibs are just x-fine, Fine, Medium, Bold, dbl-bold in sizes but don’t flex usually, although some softer nibs do flex a tiny bit and aren’t considered flex nibs. Check out the Goulet Pens nib comparisons tool and you’ll see the difference on the nibs you choose. http://www.gouletpens.com/nib-nook
Italic nibs are wide and have a slanted angle ground on the end of the nib. A stub nib is a wide nib without the slant. This lets you write thick or thin lines depending on how you’re holding the nib. These nibs also show off the shading in some inks.