An Egg's ☆ determines the maximum value of color ranges of the resulting monster. Each ☆ represent an extra maximum 100 value in the colors range. So a 3☆ egg can only hatch a monster that meets the color ranges of up to 300(3x100) only.
Found Monsters will be recorded in the monster guidebook (System -> Monster Guidebook). There the color range of the monster can be seen as blocks. Each block represent the value 0-100 in the respective places.
e.g