To be more specific, here's a quick story that I made up.
You upload your awesome photos on your computer. The photos are now on iPhoto and on your Photostream. The next day, your computer breaks/ gets dropped in water and all of those awesome photos in your computer are now gone forever.
So when you buy a new computer and set your apple ID on everything, will the photos that were on your previous computer show on your Photostream? Or do you have to start your photo library all over again?
Photostream is not a back up. It's just a shortcut to importing. Photostream is limited to 1k photos for 30 days. After either of those limits are reached the material is deleted.
So, should you end up with a submerged Mac, should your house burn down and all those other horrendous possibilities, you need a back up.
A Back up is a copy on another disk at the very least, and ideally one off-site too.
Most Simple Back Up
Drag the iPhoto Library from your Pictures Folder to another Disk. This will make a copy on that disk.
Slightly more complex:
Use an app that will do incremental back ups. This is a very good way to work. The first time you run the back up the app will make a complete copy of the Library. Thereafter it will update the back up with the changes you have made. That makes subsequent back ups much faster. Many of these apps also have scheduling capabilities: So set it up and it will do the back up automatically. Examples of such apps: Chronosync or DejaVu . But are many others. Search on MacUpdate
My Back up routine
My Library lives on my iMac. It’s Backed up to two external hard disks every day. These disks are permanently attached to the iMac. These back ups run automatically. One is done by Time Machine, one is a bootable back up done by SuperDuper
It’s also backed up to a portable hard disk when ever new photos are added. This hard disk lives in my car. For security, this disk is password protected.
I have a second off-site back up at a relative’s house across town. That’s updated every 3 or 4 months.
My Photos are backed up online. There are many options: Flickr, Picasa, SmugMug etc. However, check the terms of your account carefully. While most sites have free uploading, you will often find that these uploads are limited in terms of the file size or the bandwidth you can use per month. For access that allows you to upload full size pics with no restrictions you may need to pay.
Every couple of months I test the back ups to make sure they are working correctly. It’s very easy to mis-configure a back up application, and the only way to protect against that is to do a trial restore.