Starting grants are for establishing your own independent research group. These grants are fairly large - up to 10 M DKK. The criteria are excellence and vision. So, if you have a strong CV, can document mobility and have an outstanding idea for a large research project, these grants are for you.
Be aware that they often come with restriction in terms of PhD age and that they are very often mutually exclusive. Most foundations do not want you to hold more than one starting grant.