I've heard Google's algorithm is based on PageRank, and that it has something to do with the links to your site. Can someone explain it, and more importantly, how I can increase my site's PageRank?
PageRank (PR) is a general measure of how many links point to your page. Note that as the name implies, PageRank is based on pages not sites. So every single page on your site has its own PR - usually the home page is the highest but that's not always the case.
The more pages link to yours, the higher your PR goes. It is a weighted algorithm, so pages with higher PR will have a bigger effect than pages with low PR.
The actual PageRank number you will see is an integer from 0 to 10 inclusive. 0 usually means the page has not been factored into the PR "graph" yet. It's also a logarithmic scale so for example if it took 100 links to go from PR1 to PR2 is may take 1000 or more to go to PR3.
The best advice is not to worry about your PageRank. Just focus on getting links from good sites and creating relevant content and you'll be fine.
PageRank is part of Google's rank algorithm. You have to have links from other sites that do not have nofollow.
There is an article on seomoz.org about PageRank Sculpting that explain a lot of details how pageright is currently used by Google.
It is interesting to know what PageRank is, but in most cases unless you have a huge website that suffers from bad structure -- PR is not something you should care about.