This is related to the security that an IP address (which represents a computer in the background).
There are many vulnerabilities which an IP can face such as
Ports can be vulnerable on this IP
Applications running on this IP can be vulnerable for attacks on this IP
This IP can be spoofed on the internet
This IP may be used to relay the spam mails on messages on the net and the list goes on
best way is to test this IP with GRC.com (gibbsons) which can tell you how secure this IP is