You'll notice that throughout your Drupal installation, and these tips, that the word "node" is used a lot.
With Content Management Systems (CMS) like Drupal, nodes are the actual content within the site. They can be pages, events, forum postings, and more.
Drupal and its modules come with several node types - web page, book page, event, forum topic, and blog included.
Advanced users can also create their own node types.
A "teaser" is a shorter version of the full node. When a block for a teaser is available on the node creation page, it allows the user to have full control over the content of the teaser. This is often a synopsis of the page or the first few lines/paragraphs copied from the body.
Teasers are not available by default. You either need a module that creates them, or one needs to be added via the Content Creation Kit (cck). This is also an advanced task, as it requires setting up and customizing several modules.