Pixel graphics are shown on monitors in the RGB (Red-Green-Blue) color model. This means that each color is composed with different proportions of these three base colors. See image below on the left.
In order to print pixel graphics, the colors must be converted into the CMYK color model. During the digital printing, the colors are then composed of different proportions of cyan, magenta, yellow and key (black). This can lead to differences in appearance between the print and that which appears on your screen. See image below in the middle.
After rendering into CMYK colors, a few more color value corrections are made so as to optimize as many digital designs as possible. Depending on how close your design is to the basic settings, the colors will appear as seen in the original. (The color chart on the bottom right shows the colors on a printed fabric).
Every monitor displays colors differently according to its settings. The combination of brightness, contrast and intensity can also change the appearance of colors on your monitor.
Tip: increase saturation and contrast of your graphics file. Just when the colors of your design may seem a bit too bright and glaring on your monitor, the final result on fabrics is most likely to meet your expectations. Note: you should also consider the color of the fabrics. Colors on dark backgrounds appear differently than on white ones.