That's not a problem. Every photo comes with its own privacy settings. You can make a photo available to everyone (That's public, and includes people visiting the site who aren't Flickr members), only make it visible to people who are your friends, just to your family, to both your friends and family, or you can keep an image completely private.
Bear in mind that *you* will always be able to see every image in your own photostream.
Photos on this page will also be governed by your relationships to your contacts, and how you've set privacy on a photo. For example, you upload a photo, and set it to be visible to your family. This means that any contact of yours who you've marked as family will be able to see your photo. Other Flickr members will not.
Your public photos will show up in tag pages too, and if one of your photos is really interesting, it might come up on the Explore page too!.
Can I make a public photo private again?
Yes. The privacy setting you associate with a photo is completely flexible. You can show or hide any photo anytime you like.
If you make a photo public, other people can add it to their favorites and the photo can be blogged. So, if you decide to change the level of privacy from public to, say, 'only visible to my family', then be aware that it will be removed from other people's favorites and blog links will break.