Definitions of checkpoint, PMON and SMON

I can give you a brief description, but please consult the Oracle Concepts Guide for more information.

When a transaction reads or writes information to the database, this occurs in memory. The Oracle memory structure that holds the blocks of data is called the Buffer Cache. So a transaction that performs an INSERT, UPDATE or DELETE operation will modify the block in the buffer cache. Periodically, Oracle flushes the changes in the cache to disk. This is done so that when the database is terminated (normally or abnormally), changes to data will be there when the instance is started again. The activity of writing changed blocks to disk is called a "checkpoint."

PMON and SMON are two required background processes. PMON is the Process Monitor which is responsible for recovering processes when the user process fails. PMON does the process cleanup. SMON is the System Monitor which is responsible for recovering the system after a failure.