This is the initial database of the data source when you connect.
Edited for clarity:
If you have multiple databases in your SQL Server instance and you don't want to use the default database, you need some way to specify which one you are going to use.
If the user name that is in the connection string has access to more then one database you have to specify the database you want the connection string to connect to. If your user has only one database available then you are correct that it doesn't matter. But it is good practice to put this in your connection string.
Setting an Initial Catalog allows you to set the database that queries run on that connection will use by default. If you do not set this for a connection to a server in which multiple databases are present, in many cases you will be required to have a USE statement in every query in order to explicitly declare which database you are trying to run the query on. The Initial Catalog setting is a good way of explicitly declaring a default database.