Regarding inks, the terms 'dry' and 'wet' give a relative idea of the viscosity of the ink: wet inks flow more freely, whereas dry inks have more friction. The difference, usually caused by the amount of lubricant (depending on the amount and quality of the dye used), can be very subtle, and hard to spot, but you can feel it quite easily in your fingers, as wet inks give a smoother glide to your pen.
Wet inks, as the name implies, will stay wet for longer, whereas dry inks dry much quicker. Among other differences, dry inks allow for an improved application of details, as it is cleaner and finer. Wet inks will feather more. And if you happen to be a left-handed person, it will also facilitate sinistrodextral (left-to-right) writing, or vice versa, as the ink will likely smudge less.
Calling a pen 'wet' or 'dry' gives a relative idea of the transfer of ink. The nib is the crucial element here: wet pens will allow for the ink to flow copiously through their nibs, whereas dry pens have nibs that deposit ink less freely.
Obviously, this binary attribution - dry/wet - of what is essentially a range of fluidity is not particularly accurate.
It is now probably clearer why it is not recommended to use dry ink in a dry pen: both traits will counter each other, or, indeed, "the rate of ink-flow is likely to be too low".