With the LOW_PRIORITY keyword, execution of the UPDATE is delayed until no other clients are reading from the table. Normally, reading clients are put on hold until the update query is done. If you want to give the reading clients priority over the update query, you should use LOW_PRIORITY.
The DELAYED option for the INSERT statement is a MySQL extension to standard SQL that is very useful if you have clients that cannot or need not wait for the INSERT to complete. This is a common situation when you use MySQL for logging and you also periodically run SELECT and UPDATE statements that take a long time to complete.