The panda update happen within the Google algorithm. Google is a search engine that uses a program (an algorithm) to look through the information it has collected (its index) to find the website suited for you. The people at Google are aware that webmasters try to manipulate the rules surrounding their search engine algorithm, so that their websites can rank higher up the search engine results artificially. Google knows that one of the ways to do this is to link from places such as link farms.
If you link from a website to another website then the first website is voting for the second website (at least in the eyes of Google). The link is almost as if the first website is saying, “this website I am linking to is worth a look”. Google wants people to link to other sites organically, but some people were setting up poor quality websites, just so that they could link from them.
Other people were setting up sites that they filled with poor quality content and links. The content that they used was poorly written and fairly useless, but the page had only been created to hold a link. The links were often sold or bought in bulk for another website so that the linked website could rise up through the search engine results artificially.
Most of the link farms that used to exist are not even indexed with Google anymore, which means that links from them have no value at all. The low quality websites that still exist have such a low PageRank that links from them have little SEO benefit at all.
When the Panda update occurred, within a few months, so many link farms were kicked off of the Google that people stopped submitting articles to real article aggregators, because they thought that they were next for the chopping block.
The worst of the worst link farms were not only producing low quality content, they were stealing content from hard working writers and publishing them with no ill consequences. Many writers are not very grounded in reputation management online, and so had no idea how to take revenge on these sites. The writers who did know how to take revenge would have to spend weeks disabling and stabbing at these websites before they were decommissioned (usually out of frustration by the link farm owner). The Panda update came along and not only were these sites kicked off of the Google search index, they were also decommissioned because they became worthless.
If you do not link from websites that are of a reasonable to high quality, then your links will not be worth as much. Also, if you link from too many poor quality sites then Google may suspect that you are engaging in Black-Hat SEO and lower your search engine ranking as a result.
Better quality does not mean it has a higher PageRank, or a higher ranking on the search engines. It does not mean the website has to be perfectly optimized. It just means that the website must not break any of the Google search engine rules. It is also better if the website is related to your website in some way. A link from a daycare center to a website selling kids shoes is okay. A link from a daycare center to a website selling car parts is not so good.
Websites that have a high PageRank and Alexa Rank will be able to give links that are seen as more powerful. This is true if the high-ranking website also has content that supports the linked page. For example, a link may be considered powerful/influential if it comes from a high-ranking news website. The page it links from may have a story about shoemakers. If it has a link from that page to your website for a shoe making company, then the link will be seen as more powerful.
Just like the content of a page should be relevant to the page it links to, so should the anchor text. If the anchor text of the shoe example above said, “Asian babes” or “Free belt buckles” then the links integrity would be compromised.
There are some people who will add content to a website, maybe via a guest post, and then add a link and anchor text that is completely unrelated to the post they just added. They will often do this because the blog they are linking from is about one thing, for example caravans, but the website they are linking to is about something different, let’s say gardening services. The guest post blogger has no doubt seen that the caravan blog is very high ranking and so wants to link from it, but there is little point if the post he uploads has nothing to do with his gardening services website. Google will not ignore the link, but they will not give it much credit in their search engine index.