I'm reading Hartshorne recently. He introduces the concepts 'very ample' and 'ample' sheaf. I could understand the definitions of them. But I have no idea why they are important.
1.Is there any geometric meaning of (very) ample? How to understand these concepts?
2.Also, when we define very ample, we use the concept 'immersion' which seems not really well-behaved. Why we use embedding rather than other better conditions, for example, closed/open immersion.