Q: My computer says that it couldn't download the update, but it meets all of the requirements necessary for the Maverick installation.  Why wont it work?

What reason were you given? Here are the requirements:

Upgrading to Mavericks

You can upgrade to Mavericks from Lion or directly from Snow Leopard. Mavericks can be downloaded from the Mac App Store for FREE.

Upgrading to Mavericks

To upgrade to Mavericks you must have Snow Leopard 10.6.8 or Lion installed. Download Mavericks from the App Store. Sign in using your Apple ID. Mavericks is free. The file is quite large, over 5 GBs, so allow some time to download. It would be preferable to use Ethernet because it is nearly four times faster than wireless.

    OS X Mavericks- System Requirements

      Macs that can be upgraded to OS X Mavericks

         1. iMac (Mid 2007 or newer) - Model Identifier 7,1 or later

         2. MacBook (Late 2008 Aluminum, or Early 2009 or newer) - Model Identifier 5,1 or later

         3. MacBook Pro (Mid/Late 2007 or newer) - Model Identifier 3,1 or later

         4. MacBook Air (Late 2008 or newer) - Model Identifier 2,1 or later

         5. Mac mini (Early 2009 or newer) - Model Identifier 3,1 or later

         6. Mac Pro (Early 2008 or newer) - Model Identifier 3,1 or later

         7. Xserve (Early 2009) - Model Identifier 3,1 or later

To find the model identifier open System Profiler in the Utilities folder. It's displayed in the panel on the right.

     Are my applications compatible?

         See App Compatibility Table - RoaringApps.