Response headers seem to be a fairly hot topic over at high rankings' forum.
The debate is all about what response header to return to the browser/spider when you have moved a page on your site to another location. The 301 or 302 bit is the status code (more info on status codes and redirects). It is important because a browser/spider will interpret the status code and act accordingly. What you want both visitors and spiders to know is that the page has not disappeared, but it is simply over here on this other part of the web - for the obvious reasons that if someone is looking for it they can find the content they were after.
Essentially, there is a minor difference regarding search engine rankings if you use a 302 as opposed to a 301.
If you use a 301 permanently moved status code then search engines like Google will point all the links to your old domain to your new one essentially maintaining your PageRank seemlessly. However, it appears that those links will not help get your site out of the sandbox/aging delay filter/whatever which is where your site will likely sit for 6-12 months effectively losing a lot of search engine traffic.
All you can do in that time is try and build quality links and anything else you might think will get you out of the sandbox. This may include getting the links pointing to your previous domain changed to point to your new domain as quickly as possible.
302 allows you to maintain rankings until the new domain has aged to perfection, essentially the old domain remains in the search engine results pages and visitors are directed to your new domain with no one the wiser and your search engine traffic intact. The new domain will still need to get out of that sandbox though, just as above you can start building quality links to the new domain and point any links you can to it in order to get it free from the aging delay and ready to become your main site - insert 301 redirect about here.
So really, you can use the 302 redirect to minimise the impact of moving to a fresh new domain name, temporarily, before using the 301.
Put a link up to the new domain explaining that the site has been moved. An ugly and unsophisticated solution, but I guess it gets the job done in one way or another. Not at all my preferred method.
'Park' the domain on top of the other. 'Parking a domain' seems to have a few different explanations, but in this case I think the inference is that two domains are pointing to the same set of files on the server. In which case Google is going to pick one URL or the other in order to display the page. This solution seems fine to me as long as you are not concerned about mixed branding in the medium term. Eventually, with concerted effort, the new domain will become the preferred in SERPs.
There you have it, a few more options to consider when moving to a new domain. Personally, I like the smooth but subtle 302 followed by a 301 chaser - tasty. Some feel this option is a bit of a scam and a loophole. I like to think it helps the search engines out, preserves their results, keeps users happy etc.
I'll happily use a 302 when I am temporarily moving a domain to a new one, and when I feel I want to move it permanently to the new domain I'll throw a 301 in there. Sweet.