AWS S3 Public Object vs Private Object?

Back in S3, I have URL's to images in my bucket that I will be presenting in my application, however they are set private. When I try to click on the link, it reads "access denied". When I change the setting of the link to public, It goes through, however I've read that public access isn't the safest thing. So this is essentially a two part question,

1) What is the difference between a public and private link/Object in a bucket?

2)And how can i make a private link/object in my bucket accessible to both myself and my users?