Algorithms are formulas that search engines use to retrieve information when a searcher types in a search query. Those formulas are responsible for ranking the pages in a list of search results.
Search engines are constantly trying to improve the algorithms they use so as to get a better match between what a searcher is looking for and what they find in the search results.
Some algorithms are simply designed to improve the quality of the search results, across the board. In the case of Google, these are called 'Core Updates'. They don't target a particular type of content or a particular pattern within content.
But other algorithms, like Panda and Penguin, are created to deal with specific issues.
The purpose of Panda, for example, was to remove low-quality content (created by 'content farms') from the search results.
And the purpose of Penguin was to remove from the search results websites and pages that had low quality backlinks and unnatural backlinks.
In most cases, these purpose-specific algorithms later become part of the 'core algorithm'.
It's important to understand how the different algorithms and 'updates' work, not for the purpose of 'outwitting' them, but because they help you to understand what sort of content Google wants to see in the search results.
Here are some useful articles on understanding search engine algorithms:
By Rob Powell