It's a way to store the values in an object into a text string format. A good introduction can be found here:
http://stackoverflow.com/questions/8641889/how-to-use-php-serialize-and-unserialize
Laravel does this in the background with jobs in queues. The job is a simple class with properties (could be name, email address, message, message ID etc) - you can't put the PHP class into the database as it is, but if you serialize it into a string you can.
When it get's unserialized you can turn it back into an object in PHP and access it's properties as you would any other PHP object.
It's similar to turning an object into JSON, but with the advantage that PHP will remember the native data type of each serialized item (string, array, integer, float, boolean).
Only properties get serialized - the methods will disappear when you unserialize.
