What is it? 
"A simple tool to save web pages for reading later."

You simply add one or two "bookmarklets" to your browser, and then you can quickly save web articles for later reading/reference, or reformat the article for uncluttered reading.

Other tools offer similar functionality. Here is a recent (Jan 2012) comparison. Note the endorsement for Evernote Clearly, which is likely a better choice than Instapaper if you decide to begin using Evernote.

Extensions and Apps
Instapaper's two primary tools are bookmarklets: 
  • Read Later (found at the top of the Instapaper Extras page), which saves a link for later reference/reading
  • Instapaper Text (found at the bottom of Instapaper Extras), which reformats your current web page for easier immediate reading
Instapaper may be accessed on any device through the browser; in addition, Instapaper will send articles to your Kindle (scroll down at Instapaper Extras), and/or may be accessed through an iOS app or Android app.

Ideas for Education / Relationship to Other Tools
Instapaper (or other similar tools) may be useful to you and your students if you commonly use web-based articles as learning resources, both as a way to save resources for later reference/reading, and as a way to present the articles in a cleaner format for more focused reading. diigo is another option to consider for saving, sharing, and annotating web resources among a group.

Note that many mobile applications that access web content are designed to easily integrate with Instapaper, making it easy to save resources you come across in those applications to Instapaper for future consideration. Scroll down on the Instapaper Extras page to see examples.