A muted color is a color that has been greyed. It is also called a shade of color.
Here are your basic color words and their definitions:
HUE means color, frequently referring to the intensity of the color as to how bright it is, such as an intense hue of red.
SHADE is a color with black added. Olive green is a shade of green; burgandy is a shade of red. Black does not have to be the only added color obviously as burgandy also has blue in it. Shades can come in fairly intense hues depending on the pigment of color used.
TINT is a color with white added. Pink is a tint of red. Violet is a tint of purple. Tints can also be intense hues - consider neon pink.
In quilting the muted colors are usually greyed and softer. They do not act as accent colors. You find these a lot in small prints. Larger prints usually have one or more accent colors on top of the background colors which may also be muted. (Hawaiian prints frequently have no muted colors at all.) A typical muted print is one of large yellow or pink cabbage roses on a pastel background with soft green leaves. Many prints for babies are done totally in muted colors or else in soft tints.
Pastels (tints) are frequently both soft shades and tints. Think about a pink - a tint- that has had a drop of grey added to it - making it a shade-. It can get confusing! Everything starts with the idea that you have pigments that are pure red, pure blue, pure yellow, pure white and pure black and mix all colors from these.
I hope this helps.