The word values gets used a lot in art so let me define it as the black, white and grey tones of a drawing.
In black and white drawings, adding tones can make a big difference in a lot of ways. Tones can be used to organize a drawing and make things clear that would be a jumbled mess in a line drawing without tone. In this example, I used tone to turn a bunch of small objects all jumbled together into one thing by coloring them all the same tone. Thus one hundred plates becomes one mess and is much easier to read at a glance. The viewer can read the dishes as one thing quickly and move on to see the figure in the middle. Without tones you don't know where to look (or even what you're looking at).
Using tones carelessly can get you into trouble. Using spots of tone that are unrelated to each other can result in confusion, much like the concept behind camouflage.
The idea behind camouflage is that lots of little spots of color and/or tone break up the silhouette and shape of whatever it's covering so that it can't be seen (much like a leopard's spots or a zebra's stripes.
One good rule of thumb is to use as few different tones as you can. By that I mean use only one shade of grey (plus black and white), if you can get away with that. Some pictures require two shades of grey. Some require three different shades of grey, but any more than that and your picture will probably won't look as crisp and it will start to get muddy.
A book I read once said that one way to have a pleasing balance is to plan a picture that is one-quarter white, one-quarter black and half grey tone (spread out over the entire picture, of course, not clumped together like this). That's not always a practical plan for every picture, though, but I'm passing it along in case it helps. It does seem to be a good balance of values.
Never forget that the eye will always be attracted to the strongest contrast in any picture. If black is anywhere against white in your picture, that's where the eye will be drawn. Otherwise, it will be wherever the greatest contrast is (dark grey against white, for example, or black against light grey, etc.).
Even in the simplest of sketches, tones can be helpful for putting emphasis where you want the viewer to look, adding graphic interest and giving a feeling of space and depth.
Also tones can help tell your story. A tone with few or light tones feels upbeat and fun. A sketch with a lot of tones and heavy shading feels dramatic and ominous.
In general black and white cartoons (like the ones in "The New Yorker") don't usually have a lot of tone...it tends to "weigh them down" and they aren't as funny at a glance. A little bit of tone makes them read well without making them feel heavy or depressing.
By contrast, if a picture is filled with a lot of grey it just feels more somber, heavy and serious at a glance.
(these are from the Howard Pyle blog).
When there are dark tones that have a lot of contrast to them (very little transition between the black and white, in other words very little grey) they feel exciting and full of tension.
Here is the same drawing in three different versions so you can see what a difference tones can make in the feeling and intent of a drawing. In the first drawing a woman reacts to a door opening. She seems startled that the door is opening but not overly concerned. Within the context of a story, maybe her husband has come home early and startled her or something like that. The situation could be dangerous but the image isn't telling you that yet.
In the second one I have added tones to help organize the information and make the drawing easier to read, as well as more interesting. But the story content hasn't really changed. The woman seems startled that someone is entering but not too shocked or concerned.
In the third drawing the door opening has a much more ominous feel, due to the heavier use of tones and the use of contrasting tones. I haven't changed her expression or the staging, and both of those things would be very helpful in heightening the drama of the scene...but I wanted to use the exact same drawing each time to show how much of a difference tones can make by themselves. This time, it suggests that someone dangerous and unexpected is arriving and that the girl is more fearful than just surprised.
To be honest, I admit that I sometimes use tones to convey an idea when I know I should redraw it to get better staging or a more pushed expression. Tones can carry a drawing even when it's not quite there (but you didn't hear that from me).
The light and dark patterns don't always have to make absolute sense, you can fake them to a certain extent to get the results you want. I find I fake them mostly when it comes to giving form and depth to objects. You should follow reality when it helps you and discard it when it hurts you...the viewer tends to be pretty forgiving, I find. If about 90% of the drawing makes sense and follows the reality of how light and shadow works, you can get away with fudging the other 10%, I would say.
Anyway, that's that, now we will return to color.....