PR (PageRank) is Googles method of ranking a site. However the PR displayed on the Google Toolbar doesn't accurately reflect the actual PR Google assigns to a site, so I wouldn't place too much importance on it.
Roughly speaking it's a relfecting on the inbound links your site has, although some sites "pass" more PR value than others (some don't pass any at all).
A PR3 is good for a new site - I'd say around a PR5 was average for a year old site - PR6 is good for a SEO'd site - PR7+ and you are venturing into big site territory. Not a hard and fast rule of course, but generally bigger sites attract more links, so they have a larger PR.
Links affect your ranking - PR is a reflection of the quantity / quality of links you have, but it doesn't affect your site's ability to rank directly (an indicator more than a factor).
Toolbar PR updates roughly every 3 months (it varies) - a PR0 may mean a site is new and therefore it's PR hasn't been updated yet, but it also could mean that a site has been banned from Google. I'd be concerned if a site stayed at PR0 for a year for example, but a few months after launch is normal (varies depending on when Google updates the PR).
Have a look at other site's PR for a better idea of where your site should be. MSN is 9, Google is 10, BBC is 9 for example. Most sites aren't as large and popular as these sites though so there aren't many PR9/10's.
Another thing to note is that it doesn't scale up consistently - there's no (publicly definable) threshold to move from PR3 to PR4 for example and each "jump" up tends to take a lot more links than the previous jump.
Hope this helps.
MG