real simple explanation, serialization is the act of taking something that is in memory like an instance of a class (object) and transforming into a structure suitable for transport or storage.
A common example is XML serialization for use in web services - I have an instance of a class on the server and need to send it over the web to you, I first serialize it into xml which means to create an xml version of that data in the class, once in xml I can use a transport like HTTP to easily send it.
There are several forms of serialization like XML or JSON.