Parked domains are different domains pointing to a single website. For example, you may make a different username/account for each and every forum you register for but you know for a fact that each different name is one person (yourself). The others are just aliases. With parked domains, Let's say you own website.com, but you also own website.net, website.org, etc. You want these domains to also point to your same website.com site so you "Park" them to your primary site (which is website.com)
Sub-Domains are "minor" domains within a "major" domain. An example would be your site being hosted by x10hosting.com. Let's dissect my domain name for example:
http://srx.elementfx.com
The text colored in red would be the minor domain name while the text colored in blue would be the major domain name.
Redirect Domains are pretty self-explanatory, they redirect users to another specified location usually set up by you.