The Filter plugin is a core plugin which is always installed.
Various filtering happens on the content that the end user can edit. It makes sure that the content is safe and allows for dynamism, which would not otherwise be available. For example, it supports tokens. If you write the word year between square brackets ([year]), it gets transformed to the current year. Most of the Snap! Websites users will want to use that token for their Copyright notice which thus will automatically be updated on each January first.
Some filters are applied just before the data gets displayed. Others are run in the background. For example, you can request for a table of content to be displayed in the page. That table of content is generated by the filter searching for each header (H1, H2, etc.) and generating a table of content of 1 to 6 levels. This could get really slow if many filters need to run and are present on many pages, so we do a lot of that processing in the background since it does not need to be dynamic at the time the user accesses the page (on the first access, we may calculate a first version the slow way, though.)
The editor will let you enter such tokens in your pages.
The Filter plugin is part of the system and cannot be removed. It is important since it will check for dangerous content such as scripts found in the content. Scripts would be executed on client's computer and could, for example, send information about the computer it is running on to a hacker's robot, which may then be able to penetrate that computer and use it to do even more harm on the Internet.