A Widget is a little piece of content or functionality provided by a third party that you can add to your typepad blog.
For example, I often get asked about adding a 'contact us' form to a blog. There's a Widget for that. Want to add a PayPal storefront? There's a Widget for that. Want to share upcoming events from your Google Calendar? There's a Widget for that. Best of all, you don't have to be a geek to install a Widget.
TypePad's Widget Gallery can be found here, but here are some of my favorites:
FormSpring forms. Create a contact form. Use it to gather opt-in data. FormSpring can connect to various shopping carts so you could use it as a simple online store.
Feedzilla. Build your own custom news feed using any search criteria and display it on your blog.
Google Calendar. Display your events from your Google Calendar.
PayPal Storefront. A mini store. Displays title, price, and image for each item you want to sell.
OpenMind. Prominently display quotes from your blog. When a reader clicks on a quote they are taken to the blog post containing that quote.
Job Search. Several widgets allow you to display job postings on your blog.
ShareThis. My all-time favorite. Give your readers a single icon to click on and share your content via Twitter, Facebook, email, Digg, and more.
Lijit. My second favorite. Add a search engine to your Typepad blog. User's enter a search term, click 'search' and see all your blog posts containing that term.