I found this great article on Transactions with Table Adapters. However, this article doesn't explain why Transactions are needed or even desirable!
Why would it be worth me trying to implement Transactions alongside my TableAdapters?
Suppose that something bad happens when you are in the middle of saving something that takes more than one query to the database. What do you want to happen to all data that has already been saved when you began the save operation? Most of the developers want to invalidate the data that has been saved previously. Well.. that's what transactions are for: you encapsulate all the save logic in a transaction so that if/when something bad happens in the middle, nothing is saved.
More on the Transactions subject: http://en.wikipedia.org/wiki/Database_transaction