OFFSET and LIMIT - performance

Hello,
I'm using PGDB with JDBC. In my app i need to select only portion of all available rows. I know i can do it two ways:
1. I can use OFFSET and LIMIT SQL statements or
2. I can select all rows and then filter requested portion in Java.

My question - Does the second way significantly affect performance especially when used with JDBC?
Does the LIMIT statement do anything else then browsing/filtering rows with cursor (= the same thing i'd do in Java)?
How are the selected rows processed in select queries? Does PG select all rows and then filter them using statements like LIMIT and OFFSET or applies the statements while processing query?

Thanks for your analyzes!

JB