Your IP address is your unique location on the network you are connectted to. SO if you are directly connect to the internet and have a public address assigned direct to you system (Via and ISP) then you system lives directly on the internet and is addressable if someone can find you ip address. Many folks from what I am told, will scan blocks of address for vulnerable systems. It is time consuming but what is processor time to someone who has nothing better to do. Once you fine a vulnerable system and exploit can be run against that particular vulnerability you found. Hence the reason for Firewalls. I am not a fan of software firewalls, Just my preference) I would rather sit behind a router the is doing NAT, and has firewall technology build into it. (there are consumer grade products that are under $100.00) Also, If a person knows your IP address and they have the ability they can launch DoS attack or DDoS attack against that IP address. This usually happen with webservers since what it does is basically eat up all the available bandwidth the server would be using to answer legitimate requests by having to answer these illegitimate requests.

As far as port scanning I agree with the guys above. I do not know how accurate your scan is going to be launching it from the same host you are attempting to scan. It's link ping loop back 127.1.1.0 address which will tell you if IP is installed and working properly but will not tell you if you have a network connection to anything else...or if your TCP/IP configuration is correct...