Windows firewall: What is difference between Domain, Private and Public profile?

[grofaty]

Hi,
I am database and warehouse administrator, so not an expert on Windows. But I have set the firewall settings to only open some particular ports. But now Windows administrator has turned off "Public Profile", because this settings according to his words are not needed - he had some problem on one program he installed and not working correctly if this Public profile was turned on.

I have read some documentation, but I am still confused what are three profiles for. There are Domain Profile, Private Profile and Public Profile. Firewall port settings can be configured separately for each of this profile. But what are this three profile realy means and how can I test if setting in each of profile are successfully set and/or really needed/unneeded?
Thanks

 

[grofaty]

Current firewall settings:

http://i.imgur.com/jvZoxDu.png