A short introduction to various forms of redirects and content duplication
There are many ways you can serve your website to visitors. Instead of just serving your unique content, some use redirects, others use content from elsewhere, or even use frames to hide the original source. Hosters can be very creative when setting up an inexpensive server -- not always keeping the search engines in mind.
Redirects:
301 will keep the redirecting URL out of the index and replace it with the redirection target. Assuming you 301-redirect from www.oldsite.com to www.newsite.com, www.oldsite.com would not be indexed anymore, www.newsite.com would be indexed. A 301 redirect is a permanent redirect and tells the search engines to transfer all value to the new URL. You use this to change URLs / domains.
302 will theoretically keep the redirecting URL in the index, keep the target out (note: it's up for grabs how it actually ends up working, Yahoo treats cross-domain 302's as 301's, Google improvises. A 302 is NOT RECOMMENDED for cross-domain cases) There are very few cases where a 302 is technically correct. In our example, theoretically www.oldsite.com would be kept indexed, with the content from www.newsites.com.
There is one case where it is technically correct: when you redirect from a generic entry page to a detailed URL with user-specific parameters, eg www.domain.com -> www.domain.com/userdata?user=blabla. You can see this in many web-shops (eg Amazon).
Mirroring:
Your server serves the same content for multiple domains/URLs. www.siteA.com has the exact same content as www.siteB.com. The search engines can crawl and index both versions but will only display one of them at a time; probably the one that fits best based on the query (if you have different top-level-domains - eg .com / .co.uk - then that might have an influence on the chosen URL). Not really recommended, it would be best to put up unique content for each domain.
Many hosters use mirroring to host both the www and non-www version of a website. That is BAD PRACTICE and you should demand a proper 301 redirect to the preferred version of your domain. On Google you can now set your preferred domain, but you should still use a proper 301-redirect for the other engines and to cement your choice.
Framing:
Some hosters do this to give the client the feeling of a domain of their own. www.domain.com has a full page frame that points to some other URL which the customer has (eg www.freewebhosting.com/users/~big-fat-corp/ ). This is VERY BAD PRACTICE and will cause problems for search engines. Your target URLs will get indexed and the main domain name will not get indexed. Don't do it, pay the extra $5 to get real hosting. The problem with the obscure URL getting indexed is that should you ever feel like changing hosting, you will need to re-build all of your links again, you'd start at zero. With real hosting your content will be associated with your domain-name and all your value commulates even if you change hosters every week :-).