What is the ERC (European Research Council)? Find more information here:

-ERC website
-Euresearch: the Swiss guide to European research & innovation

Q: "authority to publish as senior author and invite as co-authors those who have contributed substantially to the work", what does it mean?

It means just  that the PI will have the right to publish independently as a senior author and decide “freely” – according to a real contribution- who should appear as co-authors. This is of particular importance in Starting Grants, as they may feel the “pressure” from former supervisors when publishing results.