Well, there are two rules there. I'll go through each of them.
I believe the following is accurate:
Rule 1
-A INPUT
Add this rule to the INPUT chain
-i eth0
This rule applies only to packets arriving via eth0
-p tcp
This rule applies only to tcp traffic
! --syn
Match packets that don't have the SYN bit set.
-m state
Track the state of this connection.
-state NEW
This only applies to new connections.
-m limit
Invoke the rate limiter.
--limit 5/m
Limit matches to 5 per minute.
--limit-burst 7
Set maximum number of initial matched packets to 7.
-j LOG
Write this entry to the iptables log.
--log-level
Set log verbosity to 4.
--log-prefix "Dropped"
Prefix the log message with "Dropped".
Rule 2
-A INPUT
Add this rule to the INPUT chain
-i eth0
This rule applies only to packets arriving via eth0
-p tcp
This rule applies only to tcp traffic
! --syn
This rule does not apply to SYN packets.
-m state
Track the state of this connection.
--state NEW
This only applies to new connections.
-j DROP
DROP packets that match the above conditions.