MsMittens is correct about IP's being insecure by default Genius.
Every time you visit a website (without any protection, such as firewalls and proxies) your computer happily hands over all kinds of information. For starters:
IP address
Operating System
Browser
Referers (previous website you came from)
It's not exactly difficult to attain IP's these days.

Like Nihil said, if you're on dial-up or DSL then this guy/girl is a blatent moron as these IP's are dynamic (they change every time you connect to the internet). At best, he/she would know your domain (range of IP addresses) which by itself is not a huge security threat unless he/she plans on attacking your ISP, in which case let me know which prison they send him/her to, I'll send him/her a hallmark.
As for cable, I always assumed those IP's were also dynamic as they're being serviced by a DHCP.(?)

Basically Genius, the only way this person could posses the ability to attack you specifically would be if he/she could pinpoint your physical computer by it's associated IP address. To my understanding, this is quite difficult with dynamic IP's (although not impossible).

My take? I'm thinking this guy/girl is trying to scare you like MsMittens said.
In any event, set up a Firewall/AntiVirus/Trojan Scanner(like the others said), notify your ISP about the threat and just keep an eye out. Good Luck.

Here's some links for you to check out to help you.
Rating the Enemy
Making your Windows OS secure
What to do if your hacked or attacked
Staying Safe Online