Say you had an Excel file with 2 worksheets you want to use to store family contact details. On the first worksheet, you have names of your contacts with their cell phone numbers. On the second worksheet, you have mailing addresses for each family with their landline phone numbers.
Now you want to print Christmas card labels to all of your family contacts listing all of the names but only one label per mailing address.
You need a way to link the two normalized sets. All the data in the 2 sets you have is normalized. It's 'atomic,' representing one 'atom,' or piece of information that can't be broken down. None of it is repeated.
In a denormalized view of the 2 sets, you'd have one list of all contacts with the mailing addresses repeated multiple times (cousin Alan lives with Uncle Bob at the same address, so it's listed on both Alan and Bob's rows.)
At this point, you want to introduce a Household ID in both sets to link them. Each mailing address has one householdID, each contact has a householdID value that can be repeated (cousin Alan and Uncle Bob, living in the same household, have the same householdID.)
Now say we're at work and we need to track zillions of contacts and households. Keeping the data normalized is great for maintenance purposes, because we only want to store contact and household details in one place. When we update an address, we're updating it for all the related contacts. Unfortunately, for performance reasons, when we ask the server to join the two related sets, it takes forever.
Therefore, some developer comes along and creates one denormalized table with all the zillions of rows, one for each contact with the household details repleated. Performance improves, and space considerations are tossed right out the window, as we now need space for 3 zillion rows instead of just 2.
Make sense?