In the last few weeks/months there have been a couple high-profile computer breaches in the news. One was at Plenty of Fish, an online dating website. The second was at HBGary, a computer security company (ah, the irony).
Plenty of Fish made a major security mistake. They stored passwords in their database in plain text. This means, if you had access to their database (legitimately or through a SQL injection vulnerability) you could see anyone's password. And this is typically a big security no, no. Passwords should always be hashed before being stored in a database.
Hashing is a one-way encryption that prevents a password (or any character string) from being un-encrypted. So, when a user logs in, you hash their entered password and compare it against the hashed password in the database. If they match, the password is the same. It is simple AND safe.
Two particular hashes are quite popular. SHA1 and MD5. Although they are beginning to be a bit dated now and, if I remember correctly, MD5 has been shown to have some vulnerabilities. Some of the more recent hashes are SHA256 and SHA512. (Use the hash function to implement them in PHP.)
Over at HBGary, the "security" firm, they actually did use hashes to store passwords. They used the common MD5 hashing algorithm. The problem with their implementation, is that they added nothing to the password before hashing it. This is an issue because people have created massive online collections of auto-generated hashes from between 1 and 12 characters (typically). So, if you have a hash, and you're a hacker, you look up the hash in this table and (if it is a normal-sized password) it will likely be found.
The best way to make this look-up table irrelevant is to add a set of constant, known characters to the password before the hashing takes place. This technique, called adding "salt" to the password, will create an extra long password, that will never show up in a look-up table. Why? Because it would take more than a lifetime to compute look-up tables that long. Hashing is an expensive operation, in terms of CPU cycles, and the longer the original text, the longer it takes to compute.
If you are building a website, and you have passwords to store, remember: salt & hash. Mmmm, sounds tasty!
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