Author's Note: There isn't much to say here; a dictionary writeup would suffice, but "mailbox baseball" is a colloquialism not likely to be found in Webster 1913. Still, since this node lacks an actual definition of mailbox baseball, I'll take a swing at it in the interest of sociological completeness.
Mailbox baseball is a game of vandalism, somewhat widely-practiced among bored teenagers who really should not be allowed around cars. It involves a team effort: One player will drive down a residential street, fairly close to the row of curb-mounted mailboxes. A co-conspirator in the vehicle's passenger position will lean out the window with a baseball bat and attempt to club each passing mailbox. The car's speed relative to the mailbox greatly increases the effectiveness of the swing over what could be achieved by a stationary vandal, raising the possibility for the mailbox to be completely destroyed.
As noted by VT_hawkeye, this amusement is a federal crime. It's also the sort of flagrant, newsworthy delinquency that local law enforcement is highly motivated to curtail. Therefore, don't play mailbox baseball. Seriously, don't.