Pagerank is formula that Google uses to judge the value of a page. The value of each page is determined by the quantity and quality of the pages linking towards it and and outwards from it. For example, if you have a page on spriggets, and many people are linking to your page because it's that useful, your page will be judged as having high value, which means a better Pagerank for you. But this is a two-way street. Your outward links also contribute to your own Pagerank.
Now, this is heavily simplified, however, it's most likely all you need to know understand Pageranking in general.
How a links value affects Pagerank: Quality vs Quantity: So, the quantity part is easy to understand -- the more links towards you the better. BUT! The people linking towards you have to have value in order to be valuable to you. If they're not high value, more specifically, if they are spam links (links purchased in an attempt to game the system), they will negatively affect your Pagerank.
Google removed the public Pagerank score: Awhile back an SEO expert could install tools into their web browser that would show a page's Pagerank. This was then used as a metric to either cold-call call clients (by claiming their rank sucked and could be improved) or by proving to the client you've done your job (by raising their Pagerank). This led to a somewhat inflated importance towards Pagerank, and people would prioritize it over other things.
Back to the post question, Is PageRank Dead? Yes... and no. If you have valuable content, people will link to you. And that's good. However, in 2009 Google removed the PageRank metric from Google Webmaster entirely. So, here's how I would phrase the answer to this question: the metric is no longer available; Google has shut it down. Therefore, I'd seriously question the intentions of anyone selling me some product or service via a Pagerank score. However, I'd still emphasize that building quality content, i.e., content that is so valuable that people would link to it, should be your #1 priority because it will positively affect your site / your business.
Side Note, Linking Scheming, a HUGE no-no. Google is very aware of the fact that there are always people who will try to game the system. And they'll heavily penalize your site for it. Some people have reported that your site can be penalized for months after you've cleaned it up.