What is a Rainbow Table?

It's a lookup table for well known passwords. For the example below the rainbow table holds the plain-text and MD5 hashed format of many passswords for quick queries.
The rainbow table I am using is Hashkiller.co.uk: which boasts of over 830 BILLION unique decrypted MD5 hashes since 2007.
Here are 3 common passwords and their corresponding hashes.
MD5 Hashes with plain-text passwords
When entering in the hashes it queries then against its rainbow table and shows that all 3 were quickly found.Obviously this isn't secure enough yet, and this leads us into the need for salting.