What is a WordPress Widget?
Widgets allow you to customize your sidebar or other widget areas (these vary with theme). There are many to choose from (check out this WordPress Widget Guide). This guide has a list of many of the widgets, what they are useful for, and screen captures of what they look like (although appearance varies depending on how you configure the widget).
Different themes have different widget areas. Go to the dashboard Appearance -> Widgets, and you will see the different widget areas. When you drag a widget into a certain space, it appears in that area on your site. Sometimes it just takes a lot of experimentation to see what looks best.
How to have certain widgets appear on certain pages
At the bottom of each widget, you can expand the “visibility” option and choose which pages that widget appears on. You might also have to go into each page (from the dashboard) and check out which template is activated within that page; this can also affect whether or not widget areas appear on that particular page.
Please reference the tutorial from the link above, and let me know if you have any questions!