garbage collector in java and finalize method

I am not clear on who has finalize method. Do we need to write it?

If you are writing a class, then you can write a finalize method and the JVM/garbage collector will call that method on your class before the object gets cleaned up/released.

You don't NEED to write this method, but you can if you need to perform some cleanup before the object gets garbage collected. But as the quote that you posted above alludes to, you generally don't need to write a finalize method, because a) resources such as sockets, files, database connections, etc should be released by your code well before a finalize() method would ever get called, and then b) the automatic garbage collector in Java automatically handles the cleanup of everything else. So there is generally nothing to do in a finalize() method.

Also why sockets database connections are non memory resources

Those are considered as "non-memory resources" because they are things that are managed by the operating system, rather than say plain Java objects which are "memory resouces" because all they require is a little bit of memory to store their variables contents.

The distinction between "non-memory" and "memory" resources is made here because generally the limits on the maximum numbers of these are vastly different. For example, if we are talking about database connections, these are generally managed by a connection pool and the maximum number of connections that are available for use might be set at say 300, whereas you might have 4GB of ram in your computer. Therefore, if you don't manage your resources properly, you are more likely to hit the limit for maximum database connections before you might hit the limit of maximum memory used.