domain vs subdomain

[brendag4]

Where can I go to find out what the differences and advantages are of having a subdomain and or a domain name?

I am not sure how they exactly work.

Is it possible to do something like...

www.mydomain.com/first (http://www.mydomain.com/first) topic
www.mydomain.com/second (http://www.mydomain.com/second) topic

instead of having to do....

www.firsttopic.com (http://www.firsttopic.com)
www.secondtopic.com (http://www.secondtopic.com)

and getting two completely separate domain names?

Is there any advantage to doing this?

Is one easier or harder to find with a search engine?

Thanks :-)