Well... When you have open ports in your computer.. Its like another door a hacker can get into..... The most common open ports usually have something called a DEAMON running on them....(No your computer isnt possesed) A deamon is a program that opens a specific port and runs a service on it.. A good exaple of this is the HTTP Deamon, the HTTP Deamon opens port 80 of your computer and runs a web server on it...... There are other kinds of deamons too....

SMTP(Simple Mail Transfer Protocol)
FTP(File Transfer Protocol)
And lots more...... If you want the full list of Ports and their services look at my other post here..... What kind of firewall you need depends on what OS you have..... If your looking for a Windowze firewall go here and check out the firewalls Hope this helps